What are some good DSLR lenses for Nikon D5000?

I have a Nikon D5000 and i'm an amateur photographer. I've been taking pictures of my friends, my cat, nature, and my band. I'm interested in buying another lens should I? What kind/what will it do for my pictures?

Depends on what you want to take pictures of.

For pics of your friends, your band, nature landscapes etc.you'd want a wide-angle lens (up to 35mm).

For pics of wildlife nature, pets, etc you'd want a telephoto (usually from 70-300mm, but up to 800mm)

Sigma is a good lens company for cheaper budgets, but I'd probably stick to Nikon's $300+ lenses, as they're more reliable and sharpers, even if they are a bit overpriced.

I think you should go with Kenko 420-800mm Super Telephoto Zoom Lens with 2x Teleconverter for Nikon D40, D40x, D60, D5000, D80, D200, D300, D3, D700 Digital SLR Cameras

KIT INCLUDES 4 PRODUCTS -- All BRAND NEW Items with all Manufacturer-supplied Accessories + Full Kenko USA Warranty:
<#1> Kenko 420-800mm Super Telephoto Zoom Lens PLUS +
<#2> 2x Teleconverter +
<#3> Precision Design T-mount Adapter +
<#4> Rear Lens Cap

I think you should go with Nikon 70-300mm f/4-5.6G AF Zoom Nikkor Lens (Worldwide), in Black

Compact and lightweight, this 4.3x autofocus zoom lens is ideal for candid shots, portraits, travel and sports photography.
Genuine Nikon product for outstanding picture quality.
Nikon HB-26 Hood (#4696, $16 value) included at no additional cost.
This Nikon G designated lens (not ED series) accepts 62mm filters.