Why the 2GB, I can guarantee that the HD 5570 will not be able to utilize it, and you will be better off buying the cheaper 1GB version. Also, how much AMPs(+12V Rail) are on the PSU, that's what really matters.
I'm assuming then you have 12v2 and 12v1, both at 14.0a. Well, that's only 168W max per rail, and probably more like 200W-240W for both combined. For that system it should be o.k with a 5570, unless it's complete crap of course .