What size filter to buy for Nikon 5100 camera for 55mm lens?

What size to buy for a 55mm lens

If you are referring to the 18-55mm kit lens, it should be a 52mm filter. You can confirm this on the lens as it should have the filter thread size printed on it somewhere.

http://www.althephoto.com

Every lens I have has a φnn on it somewhere. The nn is the thread size you're looking for, for instance my Tammy has a φ62 on the barrel, which means I need a 62mm filter for it.

Sigma EX DG 55mm Multi-Coated UV Filter blocks the invisible UV component of light from the sky, which can cause blur and to which many color films react with a blue cast. UV Filters are ideal for photography in high altitudes (in the mountains), by the sea and in regions with very clean air. The pictures gain brilliance and disturbing blue casts are avoided. Because the glass is colorless, color rendition is not altered, aside from the elimination of the unwanted blue cast, and no increase in exposure is required. The colorless glass also makes a UV Filter very suitable as protection for the front element of your lens against dust, flying sand, sea water spray and the like, and it can be kept on the lens at all times