Then you're going to have issues. That is what I used to have (I'm assuming it's the dual-core).
I was lucky to get 20 fps on that and I had a worse GPU than you: HD3870. When I upgraded to my current CPU (AMD Phenom II X3 720BE), my fps jumped to around 35 fps. When I then upgraded to the 5750, I was getting an average of 40. With my over clocking, I'm around 45 now.
So, I don't know how well a 5770 will work with the 4200+. My guess is, not much. You might get better FPS than I did, but I don't know.
You really need to upgrade your CPU to a tri or quad-core CPU because GTA IV was written to take advantage of the extra cores. Dual-cores just don't cut it very well with this game.