Delta,
i have a sapphire 5830. Its performance is almost identical to the 5770, so if i can turn all the eye candy on, your 5770 will be able to do the same and run at steady 60 fps. And my noname 500W psu runs it without a problem.
Yours may be able to run two 5770s in crossfire, and thats a kickbutt config, should perform better than a single 5870.
The 5770 can run the dx11 too, no need for the newer 6770. The newer cards only advantage is the lower consumption.