From what I've read the 5870 can pull good frame rates on graphically intense games even at very high resolutions. You may be able to get by with a 5850 depending on the games you play, the image quality you want, if you ever plan on getting a bigger monitor, and how long you want the card to last you. I have a 1680x1050 monitor and just ordered a 5870, I'll pretty much be able to play everything maxed, but I may get a bigger monitor in the future (actually I plan to buy a 1080p HDTV and use it as a huge monitor, but that's 1920x1080 which is bigger than my current monitor).
Also the 5000 series support multiple monitors (individually, 3 monitor Eyefinity, or 6 monitor Eyefinity on select models) so you should take that into consideration as well (if I do get a TV I'll probably leave my desktop+monitor at my desk and hook the TV via HDMI as a second monitor with a long cord)