Does this lens focus with the Nikon D5000?

Http://www.amazon.com/Nikon-18-55mm-3-5-5-6G-AF-S-Nikkor/dp/B0009HN57E/
It's an AF-S lens so I'm almost sure it does.
I really just want to make sure before purchasing the items.

If it says AF-S on the lens it will focus with 5100.

Yup! It's the kit lens. It has both Manual and Auto-focus.