Is the Nikon 10.5mm f/2.8G ED AF DX Fish eye Nikkor Lens compatible with the nikon d5100?

Is the Nikon 10.5mm f/2.8G ED AF DX Fish eye Nikkor Lens compatible with the nikon d5100?

Of course. Nikon AF lens, nikon camera, no problem. You'll just have to focus manually but that's not that much an issue with such a wide lens.

Since it is an AF lens (not an AF-S), you will not be able to autofocus it with your D5100.

It will not auto focus, but as the first answerer said it, it will all be very much in focus if you'll do landscape. There are other alternatives though.

Here's a Wide Angle Lens Buying Guide - http://www.the-dslr-photographer.com/2011/06/buying-a-wideangle-lens-nikon/