you need 350w but a good 300w can handle it . the max resolution is 2560 x 1600 so it depends on the monitor resolution . even if it can display on 4 monitors it wont be able to play games . you could however watch movies.
Amd cards only support up to 3 independent monitors with at least one displayport plus I doubt you will not find any 5570 with more than 3 connections. But you can have as many duplicate monitors as you have splitters. And it's 2560x1600 per monitor. A good 250w can handle it.
Edit: Starting at the 6770, there are a couple special cards than can handle up to 5. $125