I can't think of a reason to upgrade your OS just to upgrade MySQL.
But, given that you don't even have MySQL 4.0, I'd guess that you have a REALLY old OS! There may be other good reasons to upgrade. If you do, you might want to consider Centos. It's identical to Red Hat Enterprise but is free.
As far as upgrading MySQL - the safe way to do it is DON'T.
That is - don't upgrade - do a parallel install.
The place to put it is in /opt. And it's standard to install stuff in /opt in versioned directories.
On my home development machine, I run Fedora 8. Even so, there are sometimes things that I want that are newer or different from the OS distribution. For example, I run a 64-bit OS, but 64-bit Eclipse is practically unworkable. So, I installed 32-bit Eclipse in /opt. (Though I have to admit that I installed Eclipse 3.3 in /opt/eclipse. My Java run-times are in jre1.6.0_05-32 and jre1.6.0_05-64, though.
And I'm about to install PostgreSQL 8.3 in /opt, as Fedora distributed 8.2.something currently, and there are lots of goodies I want in 8.3.
I'm guessing you will need to dump your databases and re-load them for this big of a version change. (I think you might as well go to 5.0.x). All the more reason to do a parallel install.
You might want to configure them to run on different ports, and run them side-by-side, as well. This would ease any conversion process and the transition period. If you have software that has problems with the newer version, you can just continue to run it with the old one.