Will this lens work on my nikon d5100?

Will this lens cooperate with my new d5100?
Nikon 55-200MM F4 - 5.6G AF-S DX Lens

Yes it will work perfectly. It's an AF-S lens so it will autofocus.

Of course it will. Its made by Nikon for their Nikon DSLR cameras.

Edwin - not all Nikon lenses, even modern ones, will work with all Nikon DSLRs to their full capability. Specifically, the Nikon D5100 body doesn't have an autofocus motor built into it, so if you want to autofocus, you have to use a lens that has an autofocus motor in it. In this case, the lens in question is an AF-S model, so it does have a motor in it and will autofocus just fine with the D5100.