Go with the 5870, you can get it for $400 or less new in box from trusted retailers and it has about the same performance and uses considerably less power. As for the power, I'd say a 5870 would work, GTX480 might be pushing it (they use over 200W) but all I can say is try it and see. I doubt overloading your PSU will hurt your components, if anything the PSU will just shut down. If this is the case buy a new PSU.
For reference, I bought a Radeon X1600Pro probably 4 years ago when I still had an old HP system with AGP. It had a 200W PSU and an AthlonXP processor, 2 hard drives, 2 optical drives, a TV tuner, modem, FireWire card, and a floppy drive. Already the PSU was probably pushed to its limit, but I stuck my Radeon in there and it worked fine. I did buy a new PSU but it didn't fit the case so I just used the old one. It ran fine for 2 years on this setup and then I took the card out for another PC (the 200W PSU is still fine).