Your 5770 is already a very capable card.
If you make an upgrade, you need to jump several performance tiers, or you will be disappointed. Something like a 6970 or GTX570.
Also, consider that your cpu may be a limiting factor.
To help clarify your options, run these two tests:
1) Run your games, but lower your resolution and eye candy.
If your FPS increases, it indicates that your cpu is strong enough to drive a better graphics configuration.
2) Limit your cpu, either by reducing the OC, or, in windows power management, limit the maximum cpu% to something like 70%.
If your FPS drops significantly, it is an indicator that your cpu is the limiting factor, and a cpu upgrade is in order.
It is possible that both tests are positive, indicating that you have a well balanced system, and both cpu and gpu need to be upgraded to get better gaming FPS.