well i have a 6770 which i guess should be similar to your 5770 and my temp goes up-to 45 under extreme stress
if you haven't cleaned your gpu in a while take it out of your case, it should be full of dust clean it and apply new thermal paste then reinstall heat-sink and reinstall the gpu the temps should go down, i would make sure my temps wouldn't go above 70 as that might be dangerous
if all else fails increase the gpu fan speed using the ati over boost thingy