Would this lens work on my nikon d5000?

Http://www.amazon.com/gp/product/B00009XV9R/sr=8-1/qid=1286847391/

Yes, but no autofocus and no auto-metering either.

This means that 1) the camera can't focus on its own so you'll have to turn the manual focus ring to focus your image and 2) the camera can't determine how bright the image should be which means the only mode you can use it in is "M" mode. You'll have to do your own guesswork on getting the right exposure (or 'brightness').

If you want to get metering, you would need an autofocus lens, like this:

You would still need to manually focus, the lens doesn't have a motor built into it, and your camera doesn't have an autofocus motor.

If you want metering and autofocus, you need an AFS lens, like this:

This is the pro version, pretty expensive, but any AFS designated lens will autofocus with the D5000. The AFS lenses have a motor built into them.

The lens you showed would be all manual, for focus and exposure.