artifacts like that are usually from overheating, get a can of compressed air and try cleaning out your 5850, make sure your case has good air flow. Also you might want to turn up your fan speed on your video card using your ATI software. And what is your cards temp when your running games and run into this problem?
What is your cards running temp when running games?? Still haven't stated what temp its running at. Use your ATI Over Drive and check the running temp while your in game. And also check your idle temp. Should look something like this. Try turning your fan speed up to around 70% and see if that makes a difference while gaming. If not you might want to contact tech support for your card and get a replacement.