The relationship between CPU and GPU when running the game?

these components do not have direct relationships when it comes to compatibility, but to motherboards they have.

in terms of running the game, it depends on the game actually. some are cpu hungry, some are more gpu bound. they do work together and having a balanced rig is the key (though you can never know unless you have a lot of hardwares that you can swap and test

pentium D @ 2.66ghz is an incredibly weak cpu....
but the same goes for the hd 5570....
both being weak will perform at their max potential and work in wondrous harmony...
there will be no bottlenecking

but if you are going to try latest games on that rig, you are in for trouble......

They should work fine, without any bottlenecking. But I suggest saving up the money and make your own new computer. Those hardware you have ain't going to play newest games like the others said. You can make a pretty decent build with just $500.