But his i3 won't be lasting him 5+ years, at best a year or two and it won't serve for games that demand that bit more from the CPU. If the i3 was honestly that good, we'd all be sporting it over i5's and i7's, but that isn't really much the case these days.
If he just goes for say an i5 4670k, he'll be fine for a good number of years, and it won't break the bank either (not as much as what you'd fetch for most i7's).
No argument with that i3 not lasting him another 5 years, but no need for anything "K", lest you overclock. Any Haswell i5, e.g i5 4460 will be perfectly good for most anything considering the GPU-bound nature of games these days - that CPU is great value these days, and in the future, should only fall in price.
Nevertheless, any i3, gen 4 and later, which is not cache-starved, is perfectly good for most games these days. I would get a new GPU and another stick of RAM.