Some guy I saw on YouTube can scrog Blue Dream in a 4x4 with a 400w HPS but what was surprising were the size of the nugs. A 315w CMH does just as well if not better than a 400w HPS, so the answer is yes.
I have a grow tent 1/2 your size (2.5 x 5 ft) and ideally if I had two 315w CMH fixtures that would be optimal.
Having 4x 315w fixtures in a 5x5 tent is an excellent idea.