Will this lens fit my Nikon D5100 camera?

Ok it may seem a simple question but I'm quite new to photography with these cameras so I thought I'd ask.

I bought a Nikon D5100 a few months ago with the 18-55mm DX lens, (has 52mm thread) and was just wondering whether this lens would also fit my camera;
http://www.amazon.co.uk/...000O161X0/
(Nikon 55-200mm VR DX lens)

I'm asking because it was my birthday yesterday and I feel that with some of the money I have I could buy this lens to get more experience and have some more fun with my photography.
I think it fits but I'm not sure because where it says what it's compatible with it doesn't say D5100 so I'm not sure whether it would fit.

So if anyone could help me that would be great, thank you.

All Nikon lenses that have "AF-S" in their name will work perfectly on your camera. Those that only say "AF" won't autofocus on it.

So yes, that lens will work.

Are you sure that a telephoto lens is the right lens for you though? What kind of subjects to you usually shoot? A lens with "more zoom" is not a no-brainer choice, there are several different types of lenses to choose from. If you're mostly into e.g. Landscape photography, then an ultra wide angle lens would serve you better. Or a 50mm prime lens for low light and portrait uses. Or a macro lens for, well, macro.

Jens is right, AF-S lenses will be fully compatible. The 55-200 AF-S VR is a good little lens. Lightweight, reasonably sharp and not too slow on the autofocus. I used one on a D60 for a couple of years before upgrading to the 70-300mm AF-S VR. The VR version of the 55-200 lens is better than the non-VR one. VR makes a lot of difference on long lenses.

Yes, AF-S means that it has a built-in motor and will autofocus to boot.

Just about any Nikon lens you're likely to encounter will FIT, but this one allows full functionality on the D3000/D5000 series.

It will work fine. I bought one for my D5000. Works great. Even comes with a lens shade.

It will give you full functionality.