AMD state you need a minimum of a 450w PSU for the HD5770 and HD6770 (they're both the same GPU just with different HDMI ports from what I remember reading). I would suggest going to a 500w PSU to be safe, especially with the XFX models.
You will need a 6 pin PCIE connector aswell so be sure to get a PSU that already has this rather than a molex extension to the GPU. I tend to find that will cause less hassle in the long run.
If you do use your PSU and use a molex to PCIE adaptor, if you experience any trouble running the graphics card (crashes, BSOD, etc) the PSU should be your first point of origin to look at when troubleshooting.
Edited by Lifeshield - 12/29/11 at 5:04am