It says max power is 500W, its 27.5A 12V rail says otherwise. Old systems used to pull the CPU power from the 5V rail which meant that the 12V rail didn't see a super large load; these days though about 80% of your power comes from the 12V rail, all of the CPU and GPU power, along with all the power drawn by motors and most of the power feeding your motherboard. On the upside it doesn't have a -5V rail so it isn't super duper old, but i would still only treat it as a 350W PSU, which means it is good for powering a basic system but i wouldn't put any graphics card worth noting it the system with it.
The 7770 is going to want 80W for itself, ~75W for the CPU, ~50W for the motherboard, call each drive ~10W, that puts you at a bit under 250W, which should be okay, assuming the PSU isn't rated at 25C with a stupid high derating curve. Average PSU you usually assume ~5W/C over the rating so running a 25C rated PSU at 45C takes a full 100W off your rating, good ones are usually down to 1-3W/C.
I won't say for sure that it won't work, but i will say that its going to be reallllllyyyy close