You don't mention which i5 you have but most of the i5 and all the new ones have 4 cores and 4 threads which is good for gaming. The i7 has 4 cores and 8 threads, the extra 4 threads, in general, do not help much in gaming.
For example, the i5-760 has 4 cores and 4 threads, i5-670 has 2 cores and 4 threads. Even the i5-670 is not bad, at 3.46 GHz and 4 MB of Smart Cache is a pretty good processor.
You have been held back by the lack of a video card, not your CPU.