How to get a Nikon d5000 to auto-focus at night?

I'm trying to get a Nikon d5000 to focus at night so that I can take pictures of the stars but it can't recognize the stars and therefore can't focus on them. Eventually I tried manual focus but it took forever before I could get a clear picture because I can't see through the viewfinder at night?

No DSLR autofocuses well on stars. Focus for most DSLRs requires a certain level of contrast in a scene to focus correctly… And faint stars in a black sky does not provide enough contrast.

However, I really don't understand why you say it takes a long time to manually focus your lens. Have you ever even read a book about DSLR photography and lenses? I only ask because anyone who has, knows that their camera lens will focus on infinity by just turning the focus ring all the way to the high end! If your subject is more than a few hundred feet away (and stars are millions of miles away) all you need to do is manually set your lens to infinity. No need to look through your vuewfinder to do that!

I think you need to pick up a book or two about your camera and learn how to use it properly.

Not all lenses have infinity focus at one end of the movement. Some will focus past the correct setting for infinity. I don't know which lens you are using, but it is easy enough to check…

In daylight, set your camera to manual focus, and select something more than 100 feet away as your subject. Focus the camera as well as you are able… If it goes all the way to the stop, you now know how to focus on the stars. If not, you need to see how far back the lens focuses from the stop to see what to do at night.

Get a very powerful flashlight to light up the skies so you can focus

I'm assuming you have a 18-55. The answer is simple, set it to manual focus, focus on infinity indoors where you see what you do. Then take it outside.