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"
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