Should I keep battery in DSLR?

I'm using Nikon D5000. When I keep battery overnight or 2-3 days inside the camera it's always discharge. Anyone can help about my simple question?

So make sure it's fully charged.

Keeping it out won't hurt - as long as you remember to put it back in again - and remember where it is.

Some camera sit in stand by mode. Just open the end where your battery sit in. They will live in your camera and stay charged.
Just remember close it before picking them up.

Some will say yes others no. I would rather error on the side of caution.So, when ever I put my cameras away, over night or for weeks, I always pull the battery - just a habit. If for some reason the battery decides to leak, at least its not in the camera.

I agree with Jim. When I'm done with the camera for the day, I pull the battery and memory card out.

It only takes about 5 seconds to insert or remove the battery, so it's not a big inconvenience. I pull the memory card so that as soon as I get home, I download that days photos to the computer.

That is not normal for a D5000, you have a damaged/expired battery. It's good advice to recommend removing a battery when prolonged lack of use is expected, but personally I wouldn't bother unless it was going to be 3 months or more.

If you don't use the battery for long time, you should not keep the battery in the camera, the best way to store a digital camera battery is keep it in a cool environment with about 70% power in it. If you often use the camera, you can keep it in the camera.
if the battery often discharge itself, and the power reduced quickly, you must be attention, if means the battery maybe died, you need change one, here are two links that have nikon d5000 battery to sell, good luck to you

http://www.nikon-coolpix-replacement-battery.com/d5000.htm

http://www.battery-chargers.org/digital-camera-batteries/nikon-d5000.htm