Starting off with the Intel® Core™ i5-2500K; the "K" is an unlocked processor that allows you to easily overclock the processor to well over 4GHz. This ability to overclock gives the Intel Core i5-2500K a major performance advantage over any of the other processors if you use it.
As to the question of will the Intel Core i5-2500, i5-2400, or i5-2320 work in a gaming system? Yes they will work just fine, but when you look at it is only $40 US difference in prices from the Intel Core i5-2320 to the Intel Core i5-2500K and you get the ability to really get a great deal more performance it end up being money well spent.
Intel Enthusiast Team