Did you notice when it started happening if anything major occurred that could cause this? Let’s try checking the battery cycles by going to the Apple on the top left, Selecting “About This Mac,” click “System Report,” then click “Power.” In the power section near the bottom I believe it gives you a cycle count. If that is high, or if there is a message saying the battery needs replaced, it could be the battery going bad. Also, do you notice if it gets hot at all? It could be an overheating issue, but doesn’t sound as likely if it is shutting off only after 5 minutes.