Also, the benchmarked power draw of a single 7770 is 250 watts at load. The 7750 is 216 watts.
The only remaining question then is your "550W" PSU. I think you are looking at around a 300W load, might be a touch more. Assuming your 550W PSU can do that on its 12V rails you should be good.
Also, the benchmarked power draw of a single 7770 is 250 watts at load. The 7750 is 216 watts.