If I plug my Nikon D5000 into my computer, will it charge the battery?

I lost my battery charger and I don't know where to buy a new one. If I just hook it up to my PC, will the computer charge the battery?

No because the feed is one way. In fact it will drain your battery even more.

No, because the USB cable from your D5000 is only for data transfer. There's no connection to the removable battery. Your only option is to replace the charger. You could check with your local electronics superstore, or try online. Here's a couple of options you.
http://www.amazon.com/...3535svym_e
http://shop.ebay.com/i.html?LH_PrefLoc=1&_trkparms=65%253A12%257C66%253A2%257C39%253A1%257C72%253A4726&rt=nc&_nkw=d5000+charger&_dmpt=Batteries_Chargers&_sticky=1&_trksid=p3286.c0.m14&_sop=1&_sc=1

NO

Just use the battery charger the way your user manual describes and your battery will charge in a few hours. Charge it the night before you plan on using it like everyone else does

You can buy a new Nikon charger from any proper camera store. Don't even think about buying a generic one. The Nikon OEM chargers communicates with their batteries do they don't overheat or overcharge. Those two things can shorten the life of Li-ion batteries in a huge way