I was going to ask if the Thermaltake TR2 470W would be compatible with a HD5770?
Oh ok. It's not a matter of "compatibility" just a matter of enough power.
I don't trust the brand, but it should technically have enough power... if just barely.
Unfortunately, although their site tells us that they have 14A on a +12V rail and 15A on the second, they do not give us a total amperage or wattage rating for the +12V combined. And as I have come to learn, the total will vary by brand and is never as simple as (14+15)x12=
If you are on a budget, I would look at the OCZ modxstream 500W. They often have mail in rebates for reduced final cost.