Stock cooler ok with a i5-6400?

Solution
You can overclock if you have a Skylake board capable of base-clock over clocking (a Z board). If you use one and over clock, then you'd probably want an aftermarket cooler. If you were going to leave it at base clocks, then no, stock is OK.

Geekwad

Admirable
You can overclock if you have a Skylake board capable of base-clock over clocking (a Z board). If you use one and over clock, then you'd probably want an aftermarket cooler. If you were going to leave it at base clocks, then no, stock is OK.
 
Solution
No, you don't. The stock cooler is fine. If you find it's too loud, if for example you game long and hard, extended sessions, and it bothers you, THEN I'd worry about maybe something like the Cryorig H7 or H5, but really, it should be fine and pretty quiet for normal use. If you do a lot of encoding or streaming, or run other demanding professional applications that are CPU intensive, you may find you want something with a bit more performance and size, but if this is mostly an entry level gaming machine or mainstream rig, probably you're fine.