Hi and welcome to the forum. When I got my first DSLR I down loaded this from Nikon. Looks like you need an AF-S only on the D5100 if you want autofocus. I was in the same boat with the D40x when I bought a 70-300mm AF lens, no lens motor no autofocus.
Nikon has a long history of making excellent lenses and we have many different technologies used in our lenses. Here is a brief glossary of our lens terminology:
ED - The lens uses Extra-low Dispersion glass for superior image quality, especially at wide apertures.
IF - Internal Focus, focus is accomplished without the lens barrel rotating or changing length, an advantage when using a position-sensitive filter such as a polarizer.
AF-S - Focusing is driven by a "Silent Wave" motor in the lens instead of the focus drive motor in the camera. AF-S lenses focus faster than standard AF-Nikkors and are almost completely silent. AF-S lenses with a "II" designation weigh less and are generally smaller than their equivalent predecessors.
D - The lens provides Distance information to the camera electronically for more accurate light metering.
G - The lens has no aperture control ring and is designed to be used with cameras that allow setting the aperture from the camera body. G lenses also provide Distance information to the camera.
DC - Defocus Control, the optical characteristics of the lens can be altered to change the appearance of the out-of-focus elements in the background or foreground.
VR - Vibration Reduction, lenses with this feature can be hand-held at lower shutter speeds than non-VR lenses because they have a system that detects and counteracts vibration associated with hand-holding a camera and lens. (VR operation is available only with specific Nikon cameras.)
DX - The lens is specifically designed for use on Nikon digital SLR cameras. It produces a smaller image circle for more efficient coverage of the imaging sensor in these cameras, which is smaller than the 35mm film frame.
What is "ED" glass?
ED (Extra-low Dispersion) glass is a Nikon innovation designed to overcome the problems of other types of high performance glass like calcium fluorite-based glass, which is very fragile and easily scratched. ED glass reduces chromatic aberration and keeps light of various wavelengths focused at virtually the same point. This results in a more contrasty image with less color distortion.