Welcome to the Forums! I hope you enjoy building computers as much as we do.
From a purely, "will it work together?" standpoint, the answer is "Yes." As for running demanding games, the key words you have are "good settings." Maxed out? No. High settings? Probably. A mixture of high and moderate settings? Definitely.
Also, if gaming is your main objective, consider the nVidia 760 over the 7950. There about the same price and the 760 should perform better in games.
My only question:
The list of components you have seem to be from the previous generation. Is there a specific reason you chose Ivy Bridge (3570k) over Haswell (4570k)?
Hope this helps.