You can certainly make this switch. Basically you, more or less, point your installation to CentOS repositories and continue on your merry way. You'll have one major problem, though, in that all the CentOS repos seem to have their 5.x packages at release 5.9. There appears, at a quick glance, to be no 5.5 specific repos any longer.
I did this on a web farm years ago (approx RHEL/CentOS 5.3 era) but haven't since....
Make sure you have current backup of your system first, as this, like all conversions, may result in considerable localized damage in the event of difficulties. I was able to cross-grade to the same CentOS/RHEL version way back when I did this. I'm not sure what the implications of cross-grading and upgrading at the same time might be. Probably a mess, so proceed with caution.
1) Clean up yum's cache:
yum clean all
2) Download the CentOS key (I just picked one of the CentOS mirrors, you can use anyone you like http://mirrors.centos.org)
3) ... the release rpm and notes:
4) ... yum
5) Import the new KEY:
rpm --import RPM-GPG-KEY-CentOS-5
6) Remove the redhat release
rpm -e --nodeps redhat-release
7) ... and Redhat Network plugin
rpm -e yum-rhn-plugin
8) Install the RPMs you've just downloaded (make sure you don't have any other RPM's in your current directory first)
rpm -Uvh -force yum*.rpm centos*.rpm
9) Upgrade the system with packages from the new repositories:
I did this, again, several years ago and it worked exactly as advertised then. But and it's a large but, that was between the same version releases of RHEL and CentOS.
RHEL and CentOS are pretty darn stable, so this would probably still work. If if were any other non-enterprise release, I'd, without hesitation, recommend you reinstall. However, as it is.... it just might work.