There's a few options here: One is that the team has been on a mission for the last five years. Everything that has happened in TOS has passed, though albeit differently. Or it could be just a years worth of missions. In that case Khan could be very much the villain, who has escaped his fate on Ceti Alpha 5 and has returned to Earth to conquer it.
TREK IS TREK. WHATEVER THE TIMELINE!
The next TV Series should be called STARFLEET!