I have 5x5830's on a 1000w PSU with a Phenom 955 quad core. It has been running stable for a few weeks.
And the PSU is..... ?
It was on sale when I bought it...probably better ones out there.
I also have a Corsair TX-850 (ran 4x5830's fine for 2 months) and an Antec 900w extreme gamer or something like that which runs 4x5830 great but when I added the 5th card I had to add a secondary PSU on 2 of the cards to make it stable.
Find something with one big 12V rail...makes it much easier to balance the load.