Best lense to get for my Nikon D5000?

The zoom the camera has by itself is AWFUL, I need a lense with way better zoom, and preferably a lense that focuses a lot quicker. I take picture of usually just people, I don't need anything that will capture great flower photos etc.etc. I was looking at the Nikon 70-300mm, help?

One of the major problems with buying a lens of this size is the tight bottom. This won't an all around lens because 70mm will be nothing close to a wide shot and you'll end up changing lenses all the time from wide to zoom.

My opinion, you'd be much better off with something in the range of 18-200 or 28-200. If you do that you won't have to changes lenses often at all because of the range of the lens.

My guess is that your skills are not yet developed to the point where you can fully utilize the lens you have.

The AF-S 70-300 mm lens is a fine lens, but if you are having difficulty with the auto-focus on the AF-S 18-55 mm lens you have now, you will continue to do so.

ALL the Nikkor AF-S lenses are extremely fast focusing, but under certain conditions, NO auto-focus lens will focus quickly or at all. In low light, finding focus is difficult unless you have the auto-focus assist turned on. If you do not have the marked focusing points covering your focus point, the camera will focus somewhere else.

You need to spend some time learning how to use what you have before buying another lens.

There's no substitute for learning photographic skills. Just buying a specific lens or camera will not do the trick

Putting a lot of zoom range into a single lens can diminish image quality. When the lens has to cover a larger sensor size making one that does it gets harder. That is why the super-duper-zoom lenses are on compact cameras, not on DSLR's.
A Nikon 55-200mm AF-S VR or a Nikon 70-300mm AF-S VR can be a good addition to your kit lens. Nikon makes a cheap non-VR 70-300mm that is inferior quality. I would avoid it. The 55-300mm AF-S VR is okay but kind of a questionable value. It's priced between the 55-200 and the good 70-300.It has pretty good center sharpness at 300mm, and the 55-300 is a little lighter and more compact than the 70-300. The good 70-300mm will autofocus faster and have better edge sharpness at 300mm than the 55-300.