Just to give you guys an idea of the speeds I'm getting with my rig. I did a FRAPS run for just over two minutes on one of the busier missions outside (plenty of **** to shoot, eyecandy, stuff to explode etc.) With the DX11 patch and the high res textures on I get avergae 50fps (min 40, max 61) when sneaking around, 43 average (min 34, max 55) when in battle. This was on 1080P, Vsync off and everything on Extreme, when pushing to Ultra the frames drop too low to make it fun.
So Deep78, I think your 5870 should be just fine (as long as you have enough RAM I think, from the site they recommend 8GB)...
Oh, I did run my GPU clock at 975 and memory on 1100, but that should only add about 3 or so frames per second. A friend of mine has the GTX580 and he gets more or less the same framerates, except he can run it on Ultra.