I logged in as root and did the following from the terminal:

Change directory to where the downloaded file is located and run these commands to first set the executable permissions and then run the binary to extract and run the RPM file:

chmod a+x jre-1_5_0_<version>-linux-i586-rpm.bin

./jre-1_5_0_<version>-linux-i586-rpm.bin

I accepted the terms and installation began. this is what is showed:
Extracting...
UnZipSFX 5.42 of 14 January 2001, by Info-ZIP (Zip-Bugs@lists.wku.edu).
inflatUntitled 1ing: jre-1_5_0_04-linux-i586.rpm
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:xconsole_device_t on line number 164
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:power_device_t on line number 248
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:crypt_device_t on line number 287
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 371
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 374
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 391
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 392
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 393
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 394
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 397
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 416
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 417
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:httpd_squirrelmail_t on line number 562
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:squirrelmail_spool_t on line number 563
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:httpd_helper_exec_t on line number 564
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:ldconfig_exec_t on line number 619
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:sendmail_exec_t on line number 653
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:sendmail_exec_t on line number 654
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:sendmail_exec_t on line number 660
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:mysqld_exec_t on line number 665
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:mysqld_exec_t on line number 666
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:mysqld_var_run_t on line number 667
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:mysqld_log_t on line number 668
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:mysqld_db_t on line number 669
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:mysqld_var_run_t on line number 670
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:mysqld_etc_t on line number 671
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:mysqld_etc_t on line number 672
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:dnssec_t on line number 683
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:named_checkconf_exec_t on line number 685
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:named_log_t on line number 691
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:dnssec_t on line number 700
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:nscd_log_t on line number 714
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:ntpdate_exec_t on line number 720
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:portmap_helper_exec_t on line number 730
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:portmap_helper_exec_t on line number 731
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:postgresql_exec_t on line number 735
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:postgresql_exec_t on line number 736
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:postgresql_exec_t on line number 737
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:postgresql_db_t on line number 739
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:postgresql_db_t on line number 740
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:postgresql_var_run_t on line number 741
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:postgresql_etc_t on line number 742
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:postgresql_log_t on line number 743
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:postgresql_log_t on line number 744
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:postgresql_log_t on line number 745
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:postgresql_db_t on line number 746
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:postgresql_exec_t on line number 749
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:etc_mail_t on line number 771
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:sendmail_log_t on line number 772
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:sendmail_log_t on line number 773
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:sendmail_var_run_t on line number 774
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:sendmail_var_run_t on line number 775
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:winbind_exec_t on line number 814
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:winbind_var_run_t on line number 815
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:samba_log_t on line number 817
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:samba_etc_t on line number 818
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:samba_secrets_t on line number 819
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:samba_secrets_t on line number 820
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:samba_var_t on line number 821
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:winbind_var_run_t on line number 823
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:cert_t on line number 863
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:cert_t on line number 864
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:cert_t on line number 865
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:system_dbusd_var_run_t on line number 892
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 900
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 901
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 902
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 903
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 904
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 905
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 906
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 907
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 908
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 909
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 910
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 911
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 912
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 913
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 914
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 915
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 916
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 917
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 918
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 919
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 920
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 921
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 922
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 923
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 924
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 925
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 926
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 927
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 928
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 929
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 930
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 931
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 932
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 935
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 936
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 937
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 938
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 939
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 940
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 941
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 942
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 943
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 944
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 945
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 946
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 947
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 948
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 949
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 950
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 951
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 952
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 953
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 954
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 955
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 956
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 959
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 960
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 961
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 962
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 963
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 964
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 965
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 966
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 969
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 970
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 973
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 974
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 975
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 978
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 981
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 982
/etc/selinux/targeted/contexts/files/file_contexts: invalid context system_u:ob ject_r:texrel_shlib_t on line number 983
/etc/selinux/targeted/contexts/files/file_contexts: invalid context root:object _r:texrel_shlib_t on line number 995
Preparing... ########################################### [100%]
1:jre ########################################### [100%]

Also on boot before I installed Java, I noticed some of this text in the /etc/selinux/... on lines in the 900's What does this mean? Any help is greatly appreciated since I'm a newbie

For Java, I would recommend you just download the normal .bin file (not the RPM one). This is because the normal .bin file extracts a folder structure that you can simple copy, link to, and have java running fine. So download that, extract it, and it will create jdk1.5.0 (or a similar directory). Move this to a standard place (such as /usr/share/) then link (ln -s) the java binary in jdk1.5.0/bin/java to your usual bin directory (normally /usr/bin/ for this kinda stuff).