Sure, you can easily remove apache and mod_perl from RHEL 4. Then install the versions you want. Probably from source, however. Not sure of rpm compatibility.
But as for Perl, that'll be a bit trickier as many things us the Perl rpm on RHEL.
I've had many, many applications running on Perl 5.6 and moved to Perl 5.8 with absolutely no issues.
Really though, if your app currently runs quite nicely under your old Apache and mod_perl, it'll more than likely run same or better with the updated versions. Plus, think of the fixed bugs and security issues in the newer versions.