I think the D5100 does not have its own focus drive motor. So any lens you get will need its own focus motor or you will need a manual focus gear for the lens.
There are any number of lenses that can be used for underwater photography. It depends on just what kind of shooting you do.
A big favorite is the Tokina 10-17. It is a fisheye lens. It is great for landscape shots and also good for taking photos of divers. You can use it on very large fish but even then you have to get close. Interestingly enough, I have found that it works well as a lens to take boat photos with. The wide angle and the depth of field make for easy shooting. I have this lens. Because of the close focus, you can shoot this lens with a 4" dome. What makes this lens shine is you can focus really close and still have tremendous depth of field. You can have a small subject in the foreground with the reef in the background for really cool shots. The big advantage of the wide angle is that the closer you get to the subject the less water you shoot through and the sharper your image (unless you have really clear water).
Another popular lens is the Nikon 60 mm 2.8 AFS micro (actually macro lens). This is a true macro lens meaning it allows you to get close enough to get an image on your sensor that is the same size as the subject. However, to do that you have to get really close. In many situations, it is just not practical to get that close to the subject. The subject is too wary or it is in a hole or something and not that accessible. Being a prime lens, this lens has a very high optical quality. This lens can also work as a sort of "long" lens for medium to small fish. Large angel fish are a bit too large. You can shoot this lens with a flat port.
Another option is going with a rectilinear lens. These lenses are zoom lenses and usually range from 10-20 or 12-24. A fisheye lens will bend all the straight lines in the photo. I don't really mind. But some people really hate the effect. So you might think of a rectilinear lens. The problem with most of these is they don't focus that closely so they need a big dome to shoot with (like an 8" dome). These lenses are good for over under shots, for diver photos and for photos of large fish.
Yet another lens is the Nikon 105 2.8 AFS micro lens. This lens does not focus as closely as the 60 mm micro but it does still allow a one to one image and true macro. It has superb optics and like the Nikon 60 mm lens is far superior optically to anything else on this list (or so I am told). The nice thing about this is that you can shoot more wary subjects and you can stand back and shoot into inaccessible spots. It would also be good for shooting small pesky fish like small damsel fish. The longer stand off range allows you to use a wet diopter lens with it to produce "super macro" shots. Super macro are ultra closeups. It is for subjects that are less than 1 cm long (about 1/3 inch).
If you have noticed, none of the above lenses really works well taking shots of fish ranging from about 8"-30" or most of the ones that you see. You could use a Nikon kit zoom for this like the 18-55 with a large dome and a diopter. Or you can use the Sigma 17-70 macro lens. This lens is very flexible. It is probably the best lens for these intermediate fish out there. It can even be used, in a pinch for landscape & diver photos and close up photos but not one to one. Of course, it will not do as good a job as the 60 mm at close ups or the Tokina 10-17 for wide angle. But it is a pretty good lens and you could use it for all of your photos starting out. But that depends on what kind of shots you are going to do.
Obviously, if you want to take shots of divers and landscapes, get the Tokina 10-17 or a rectilinear lens (if you don't like fisheyes). If you are into close ups of small critters, all you will need is the 60 mm and/or the 105.
If you like taking photos of moderate sized fish, you might think of the Sigma 17-70 or a kit lens.
As you can see, there is a whole world of options. On dive boats, I often see DSLR photographers shooting with different lenses each day for obvious reasons.
I would recommend that you get a couple of good strobes as well. For macro photography, you don't need a really powerful strobe. But for wide angle photography, you tend to want more power. You want a strobe because you lose all of the red light in the first 15' of the water column. If you want true colors, you have to take down your own light source. Also, it is nice to have a focus light for shooting under ledges where things are dark. Things add up quickly.
