Core i5 processors are good for gaming.
An Intel Core i5 2320 is a product of the 2nd generation core i5 processors (named "Sandy Bridge"), and it has turbo boost.
Any of the Intel Pentium G-series processor are not recommended for gaming... They are slow processors.
If you are going tu purchase a new Intel Core i5 processor, I suggest you to get a 3rd generation one (named "Ivy Bridge"). It has a better integrated GPU, better clock speeds and new awesome features.