Will my Nikon D5200 autofocus with a Nikon AF-S 18-135 lense?

Will my Nikon D5200 autofocus with a Nikon DX AF-S Nikkor 18-135mm 1.3-5.6G ED lense?
I have a Nikon D80 at the moment but i'm getting a D5200 for my son. Will the lenses I have work and fully auto focus with this camera? Do I need an adapter? What lenses do I need to buy for it to work?

Yes, the D5200 uses AF-S (motorised) lenses.

AF lenses need a motorised body, they will fit - and meter with - both the D80 and the D5200, but won't allow autofocus. Any Nikon body will autofocus with AF-S lenses, motorised or not.