What graphics card do you have now? A 400W PSU, even if fairly weak (i.e. really a 300W PSU with a liar-label) should have no trouble with a HD5670, which needs no auxiliary power.
That's not a really great bang/buck card though, even if it is a big improvement over what you have.
Knowing your budget, and guessing your monitor resolution is 1680x1050 or lower, in your place I would spend $50 on a 430W Antec Earthwatts PSU: http://www.newegg.com/Product/Product.aspx?Item=N82E16817371034
and then spend another $130 for a HD5750: http://www.newegg.com/Product/Product.aspx?Item=N82E16814150448
for a substantial performance improvement, and two parts you could carry over to your next build.
Edit: The 430W Antec Earthwatts would have no trouble with a HD5770. You do not need a 650W PSU for that card. You could actually run a HD5850 on it, although not comfortably. If you want to get something like a HD5850, stretch your budget enough to fit the 500W version of the Antec Earthwatts.