So I'm going to buy a new computer, It has an AMD processer with an integrated ATI Radeon HD 5670 graphics card. But from my old computer I also have an ATI radeon 4550 graphics card. It's not a huge deal but is there any way I can run them simultaneously?
Yeah, unless the card and board are specifically designed to be able to work together, you can't use them in SLI. And even if you could the higher card would have to step down to the speed of the lower card in order to be able to sync frames.
You don't need the same card, but using different cards is kinda weird, the fastest one is called the master and the slowest one is the slave. If you need extra power the master will use the slave's capabilities to help him out, but this is complicated shit and for maximum performance 2 identical cards are better.