You'll need to first find out if your current motherboard will be able to support your graphics card - is it equipped with AGP? or PCI-E?
Next, you'll need to see if your power supply will be able to provide enough juice for your card - 500W is good enough for most cards, for high end cards or overclocking you should get something 600W+.
Then there is the issue of the graphics card fitting your case. If you're looking at the HD5870s and HD5850s, those are big cards that probably won't fit in a small tower or mATX sized motherboard.
Of course, if you're looking for a fully optimized system, there are additional factors to consider, but I won't burden you with them anymore.