Now I need to install install Intel Fortran Compiler on my Linux system, the information about my system is:
Linux localhost.localdomain 2.6.18-53.el5xen #1 SMP Wed Oct 10 17:06:12 EDT 2007 i686 i686 i386 GNU/Linux

In the process of installation, an error always appeared:
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Intel(R) Fortran Compiler for applications running on IA-32, Version 10.1 (10.1.015)
Installing...
Installation failed.
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RPM std error output is as follows:

--------------------------------------------------------------------
error: Failed dependencies:
libstdc++.so.5 is needed by intel-ifort101015-10.1.015-1.i386
libstdc++.so.5(GLIBCPP_3.2) is needed by intel-ifort101015-10.1.015-1.i386
--------------------------------------------------------------------

This failure occured using the following RPM options:
-U --replacefiles --force


--- WARNING ---

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At first, there is no libstdc++.so.5, it is libstdc++.so.6 when install the Linux system, but after I install libstdc++.so.5, it still remind the same error as above.Please give me some suggestion about that, Thanks!

The RPM must be looking for the library in the wrong place if you installed it. How did you install it, and did you replace any links to libstdc++.so.6 with libstdc++.so.5?

How did you install libstdc++.so.5? Which package? What is the output of the following command?
this should tell you if the shared libraries cache has been updated after installing libstc++.so.5.

First, I download libstdc++-3.2.2-5.i386.rpm.
Second, I install it: rpm -ivh --nodeps libstdc++-3.2.2-5.i386.rpm

When I use the code:/sbin/ldconfig -p | grep libstd
[jing@localhost ~]$ /sbin/ldconfig -p | grep libstd
libstdc++.so.6 (libc6) => /usr/lib/libstdc++.so.6
libstdc++.so.5 (libc6) => /usr/lib/libstdc++.so.5

I am not sure whether the installation is successful.

Thanks, I install it by this code:
rpm -ivh --nodeps libstdc++-3.2.2-5.i386.rpm
By the way, do you know how to check the links to libstdc++.so.6?

Intel does list: compat-libstdc++ providing libstdc++.so.5 as a system requirement - dunno if it makes a difference if you install compat-libstdc++ or libstdc++.so.5 directly.

Only experience I got is with the intel c compiler on gentoo and that uses libstdc++.so.6 - works w/o a hitch.

I was thinking of ldconfig, but you could also look to see if there are any other symlinks pointing to .6 that you at least temporarily change to .5; You didn't actually say what distro you're using - that might help someone else with experience in this particular case to help.

It looks right. Have you tried to install ifort again?

I have tried to install IFORT again, but the same error is appeared. it is really a tough problem.

As already pointed out by crashmeister, you have to install the compat-libstdc++ package, not an old libstdc++ which can be not compatible with recent gcc and glibc.
Better to use the package manager of your system to retrieve the proper package from the available repositories. If using RHEL, try up2date from the command line.