Or Is it possible to install Perl 5.10 as non-root under my home directory?

Most certainly! Perl does not require it's installed as root (I usually install Perl using a dedicated uid), nor does it require any specific place to be installed.

Just download the tarball, unpack it, run ./Configure -des -Dprefix=/path/to/install/location && make && make test && make install, have a cup of coffee, and you're all set. (Just make sure /path/to/install/location exists by the time make install runs).