Hard to tell, itll probably be pretty close. Your ``500w´´ PSU cant even deliver 300w on the 12 v rails. If it can even deliver the rated wattage it will be pretty much under 100% load if the cpu and GPU are stressed. You could try running prime 95 and furmark simultaneously with your current setup, if your psu doesnt shut down or catches on fire itll probably power the 7770 in games, though its not advisable.
It would probably be the best to get an inexpensive proper psu like a evga 500w or a xfx 550w and a 7850 2 gb or something similar ( for low cost 1080p gaming with high settings).