Is it possible to manually focus during a video using the Nikon d5200?

Or is autofocus the only way?

Yes you have the ability to switch from auto to manual focus while you are shooting video.

All you need to do is simply move the Auto Focus switch on the side of the lens from A to M. Its the same on every other Nikon DSLR to when it comes to shooting video or taking pictures.

Have you noticed the AF / MF switch on the lens? That's where you turn off the AF. Then you turn the focus ring yourself.

Yes. You can manually focus during video. There's a switch for AF and manual focus on the body and sometimes on the lens itself.