I always go by the rule of thumb of getting the fastest CPU that I can afford. The i5 is great for gaming while I feel the i3 would be a bottleneck for some games. Depends on what you play, I play a lot of MMO's like WoW, BDO, GW2, WoT, so its more cpu intensive and having an i5 would help on those. Even with standalone games like Witcher 3, The cpu really helps with framerate.
I did an accidental test of cpu speed, was messing around with the overclocking of my cpu and forgot to set it back to original settings or save my settings and it locked itself at 1.5ghz, even with a GTX 970, i was getting 20-25 fps on BDO where i usually get over 80fps. Took me a while to figure out what was wrong until i check my cpu settings, once i had it back on stock configs, FPS went back to normal.
Its gets a lot more technical than I can explain about CPU its core, threading, etc... so I just get the best CPU i can afford