To be honest, GTA4 and the add-ons are heavily CPU-limited, so even if you get a HD 5770 the performance boost may not be as big as you would imagine. Therefore if you want to see a big improvement in the game then I would strongly suggest investing in a new CPU (and then overclocking it as well). You can get a Core 2 Quad Q6600 (G0 stepping) for around £70 second-hand these days - this will overclock well and provide a massive speed boost in GTA 4.
Also, instead of going for a HD 5770, I would suggest the much more powerful
HD 5830 for £90 - your PSU can certainly handle it.
This chart shows how it compares to a HD 5770.
Also, if you can stretch the extra £18 to get a
HD 5850 for £108 then the performance jump is impressive (have a look at
this chart comparing it to a HD 5830).