My faithful 3 year old 8800 GTS 640 gave out on me today. Going to replace it at microcenter tomorrow and these two cards are what I am deciding between. The 5770 is $200 and the gtx275 is $220. I am running an ASUS P5K motherboard (nforce chipset) with a 500W power supply (CPU is a Q6600).
Resolution: single monitor 1920x1200
Main Games: Source Engine Games, Mass Effect 2, Batman Arkham Asylum, Crysis
So if you don't replace the PSU, I wouldn't get the 275.
I ran a 4850 (115-150W Max) on a poor 550W, so the 5770 will probably work on your PSU. However, I suggest getting a new PSU if you can. If a PSU dies, there is a good chance it will take down other components with it.