Okidoky, so, I have a Powercolor Radeon 9550 se with catalyst version 4.x (I'm not 100% sure). Anyway, I got a DVD with a gaming magazine which had Catalyst version 5.6. I decided to install it, and all was fine, until a few minutes later when clicking on a certain menu link in a game of mine (TM Sunrise) caused the computer to suddenly reboot itself. I tried the game again and the same thing happened. I decided to reinstall the adapter's drivers from scratch from the cd supplied with the card, and it fixed the problem. The question is, is there a certain way to install newer drivers for graphics cards, or are the latest drivers just too advanced for the video card that I have?

Yep, you make sure the previous drivers are uninstalled beforehand via Add or Remove Programs under the control panel. If you still experience issues, try older versions or the alternative Omega Drivers.