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.
The 4460 will do him some years as well, though I don't see why he has to always be cheap in his options. I'm not advocating he absolutely splurge, but I;m not saying he should be skimping out on the core parts either.
Also don't forget about some recent CPU itensive titles like Ashes of a Singularity or Total War.
If he gets another stick of RAM and a GPU, he'll eventually need to swap out for a CPU, one that fits with a new mobo, and we know his build is already dated, so that adds to the cost. THe more you hold back on a part that is cruicial, the more it ends up having you swap out more down the line.
Step right up come on in, feel the buzz in your veins, I'm like an chemical electrical right into your brain and I'm the one who killed the Radio, soon you'll all see
So pay up motherfuckers you belong to "V"