Hi Bradley,
To upgrade your Mac OS X to 10.5 would be done buy buying a copy of Mac OS X 10.5, and installing it on your system.
But your system would also run happily with a newer version of the OS too, including Mac OS X 10.7. That version is actually downloadable from the Mac app store, so you could just download it and install it... - well, that would need Mac OS X 10.6 installed on your system. But they do have Mac OS X 10.7 as a separate install media, a USB drive
http://store.apple.com/us/product/MD256
That would however still leave with the problem of first having to upgrade to Mac OS X 10.6, but in practice I've seen 10.7 been installed directly on Macs with 10.5 on them.
Updating your system to Mac OS X 10.5 probably would cost more than going to Mac OS X 10.6 - Apple still sells 10.6 for $29 whereas the older version may be harder to find. (the older version will still be popular with some Macs that are older than yours and would not run e.g. with 10.7, so I'd say you are better with 10.6 or 10.7)
http://store.apple.com/us/product/MC573Z/A?fnode=MTY1NDAzOA
So Mac OS X 10.6 for $ 29 would be a good way to update your system.
And from that whenever you'll decide or want to upgrade to Mac OS X 10.7, you can do that for another $ 29. If I remember right, when 10.5 was the newest OS, to update to that would have cost you back then $ 129 so compared to that, it's way cheaper, and definitely worth it.
