Well, your 5570 is NOT the fastest card in the world. The lowest you should go would be a 5750 (which is what I have) and that is possibly the lowest gaming card you should have.
A 4870 outperforms the 5570 and that is probably your main issue. 5570's are not meant for gaming. Also, how much memory is on the 5570? These days, you need a minimum of 512mb but you should really try to get a card with 1gb of dedicated memory.