No - not enough power. When you buy a replacement provide for some future upgrades and additions. Also, the capacitors will age and all PSUs will gradually deteriorate in perfomance.
That's very true though he was asking if it would work to begin with. I personally don't recommend that psu as 29A is a gamble given the efficiency of the psu is 70% so it won't really produce as much power over time as you said. But according to a similar thread, http://www.tomshardware.co.uk/forum/292314-15-amps-requirements-radeon-5770/
it should work just fine with a Sapphire Vapor-X 5770 overclocked.
I think what he should be asking instead is whether it will run just a basic system with a 5770 or a fully loaded one with several drives, fans & other peripherals and overclocking as well. If you ask me, it is a stepping stone for now but he should definitely consider another power supply for it later on.