Well, 2-3 hours per day every day may end up in issues if the 5770 is maxing out what your power supply can output. That being said, it's why purple stank suggested in getting a 5670.
Depending on what your resolution is, the 5670 should manage most if not every game at 1280x720 with 4xAA+/1680x1050 with 2xAA.