5770 uses about 90-115W at Max.
GTX 275 is about 160-220W Max.
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.