Both cards and motherboard PCIe slots are forward and backwards compatible.
Your only concern is a proper power supply and making sure the card physically fits in your case.
If its for gaming, make sure to check out the benchmarks and see if it's much better than what you already have.
It's obviously not the top card but it is better than my HD5870 which ran every game quite nicely though not necessarily maxed. (Diablo 3 is very well coded and never dropped below 60FPS, maxed at 2560x1440. BF3 on the other hand had to be played on medium).
My current recommend for some is the GTX670 but I'm not going to tell you what to do as it depends so much on the games you play and your budget.
(Love my new Asus DirectCU II GTX 680. It just arrived a few days ago. Batman AC still stutters but most everything else is a huge improvement over my HD5870 except for games that were maxed already like Diablo 3.)