"do NOT get a 1GB HD 5770. No card that is less powerful than the HD 4870 can use 1GB. The 4870 can BARELY use it and only in Crysis at super high settings with 8xAA. Get the 512MB HD 5770. The manufacturer is just trying to get extra money out of you. The HD 5770 is not powerful enough to even function in a situation that uses 1GB."
Thats not a reference 5770, it does not have eyefinity or as you notice 1gb of ram. That card goes on sale for 130.00 and is about what its worth. I would spend the extra 15 dollars and get a 1gb version. There are games that might suffer a little at higher resolutions with only 512 and the power the 5770 can deliver. Its a card such as the 4850 where one can get by in most cases with 512, but there are situations where the 1gb would perform better even there.
edit: 4870 and 5770 are both good choices for your cpu. There is no reason to get the 4870 when its at the same price as the 5770. Even if its 10% faster.