you are aware that the current OLDER rhel5 is RHEL 5.10
and you are 7 minor upgrades behind
and that the current version is RHEL 6.5
well ALL of those backup archives can be deleted
it looks like you never configured "logrotate"
http://linuxcommand.org/man_pages/logrotate8.html
also the old backup bootlogs
boot.log.1 through boot.log.4
the bad login
btmp.1.gz through btmp.1024.gz
and with this rhel5 install
missing the last 7 operating system upgrades
and there for WIDE OPEN to the last 4 years ( since 2009) to ALL of the NOW FIXED security holes
if a system that is missing 4 years of updates ,is misbehaving, my FIRST guess will be that you have been comprised .
that and that the log folder is eating ALL of the drive space with old back-ups