The HD5770 will perform quite well at that resolution but on the more intensive games you will probably want to turn AA down or off. On the most intensive games(Crysis, Metro 2033, Stalker, BF:BC2, ect.) you will need to turn down some actual settings. If that doesn't sound good enough for you then grab an HD5850 if you can afford it. If not then, assuming your motherboard can handle it, you can add another HD5770 in crossfire later on for performance similar to an HD5870.
The processor is fine though an overclock and/or unlocking the 4th core(if your motherboard allows for it) will help performance in the more CPU intensive games. The chip OCs quite well and the odds of the fourth core working are pretty good.