The 5770 is a very efficent card. I'd think your psu could run it. Its always good to have a quality psu though. (Brand and amps are more important than watts).
I believe the 5770 uses around 100w loaded with around 9 amps? Try google 5770 amps. Id do it if I wasn't on my phone hehe.
You can always try it out and if you don't like the results then upgrade your psu.