2) In some games CPU doesn't matter. These are GPU limited games. See chart below
Most of the games available today are GPU or graphics intensive games. They put much stress to GPU. 4GB or more RAM is sufficient for running system without lag, but a GPU ensures how smoothly you will be able to play games. That is why we need costly GPU with enough horsepower to handle all the eye candy a game offers.
Some GPU comparison chart. The HD6670 is slightly faster than HD5670.
All benchmarking was done at high settings. So you see it is highly recommended to buy at least a HD7750 (which is much powerful compared to HD5670 or HD6670) for smoother gameplay & as a gamer I assure you 30+ FPS is smooth enough, you'll not be able to notice the difference between 30+ FPS & 60+ FPS in most cases.