Scientific Linux was designed so that an administrator can easily upgrade their computer between minor releases.
It is not required that administrators upgrade their release, because the security errata will be updated for all releases. But there are often features and/or packages included in later releases that were not available with the earlier releases.
Below is the steps, for both yum and apt, to change to the latest 5.x release.
These instructions are for updating between minor releases, such as from 5.0 to 5.1. Changes between major releases 4 and 5 (such as from 4.2 to 5.1), cannot be done with yum, but must be done with the main installer.

YUM

For The Impatient

1. x86_64 only yum remove perl.i386 gaim.i386 gaim-devel.i386
2. yum clean all
3. rpm -Uvh ftp://ftp.scientificlinux.org/linux/scientific/5x/i386/misc/RPMS/yum-conf-latest.SL.noarch.rpm
4. yum update yum
5. yum update

For those a little more cautious

1. Make sure you have done your backup's.
   I haven't heard of anyone needing them, but don't you be the first.
2. Make sure you have enough disk space. In particular, make sure you have enough space in /var/cache, which is where yum downloads the rpms.
3. x86_64 only yum remove perl.i386 gaim.i386 gaim-devel.i386
   In earlier versions of SL (5.0, 5.1 & 5.2) there was a i386 version of perl and gaim in the x86_64 release. This was taken out by the upstream version, and eventually out of SL. In order to update to newer versions of SL, you need to take the i386 version of perl and gaim out of your x86_64 install.
4. optional yum update
   This will get your system up to date with the latest packages. It will also make the last step smaller.
5. yum clean all
   This cleans up all the headers and packages from your old yum configuration. If you do not do this step, it is very likely that yum will say that there is nothing to do.
6. rpm -Uvh ftp://ftp.scientificlinux.org/linux/scientific/5x/i386/misc/RPMS/yum-conf-latest.SL.noarch.rpm
   This will install the latest yum.conf for your system. If you customized your yum.cron, or your yum.cron.excludes files, these will not be touched.
7. yum update yum
   It's always good to have the latest yum before doing this, just incase the latest yum has fixed some bug you would have run into.
8. yum update
   This is the big part, where everything gets changed.
9. Check your grub settings. Although yum usually get's things right when it updates kernels, it is always a good idea to give the grub config file a check.
10. optional yum clean all
    This cleans up all the rpms that you just downloaded, clearing up your disk space.
11. /sbin/reboot
    Reboot into your new kernel and Scientific Linux release