At the 1080p resolution of your TV you are looking at medium settings for most of the games you listed. You might be able to creep into high in Fallout 3 if you use no Anti Aliasing. BFBC2 is probably going to give you the most trouble. It is the most graphically demanding game on the list, and is also very CPU heavy, it's recommended to have a quad to try high settings on that game. On low or medium you should be okay, though you probably will be looking at about 30FPS as your framerate, and it may dip lower if things get really busy on the screen.
If you want high settings on a 5670, 1280x720 would be more appropriate, though depending on the TV, you may take a big hit in picture quality if you go that route.