Some folks like CentOS as compared to RHEL because of many reasons. Mainly because of easy to update from its internet repository this is maintained by itself.
But as in every migration, there is always be risk factor about the various running applications on your present setup. You should always test it on some test beds before going to do it in any crucial setup and backed up everything to which you are caring about.

Steps of migration and update

# cp /etc/redhat-release /etc/redhat-release-saved
# rpm -e --nodeps redhat-release-notes redhat-release yum-rhn-plugin redhat-logos
# rpm -ivh centos-release-notes-5.9-0.i386.rpm centos-release-notes-5.9-0.i386.rpm redhat-logos-4.9.99-11.el5.centos.noarch.rpm
# yum update

After doing these steps it will ask for confirmation for update, you can confirm for download and update various update packages from yum repository. And after all check you system version.

# cat /etc/redhat-release
CentOS release 5.9 (Final)