Although not fully tech, here is what happened to me today...

I got out from class and went to get a bite to eat about a mile away. My car started fine. I run in for 5 minutes to get food, come back out, and my car wouldn't like to start. The radio didn't work, the dummy lights were dim, and my clock didn't work. I figured it might be the backup fuse. All my fuses were good. So I had a couple of people push start me, and my car fired right up. This eliminated my suspicion of the main relay (replaced less than a year ago) since I didn't hear the fuel pump priming. I bought a new battery and everything was back to normal.

I was wondering if it was common for batteries to take a **** in 5 minutes.

 

My guess is you have a bad alternator. If the battery had enough juice to start the car and then 5 mins later after running just down the road wouldnt come close to starting, your car was running solely off the battery for the short trip. Meaning the alternator wasn't charging the battery.

Check the alternator before you get stuck someplace.