iPhone 5 died even though it was at 60 % battery

This is what happened: I charged the phone before I left, and it was at 60 %. I hung out with some friends for a few hours, without using my phone. Then as I was walking home, I started listening to some music, and took a couple of photos with the iPhone camera. Two minutes later and the phone just died on me. I have no idea what happened. The music just stopped, it went black, and the charging symbol started showing. I tried to click on the start button, the restart button etc, but nothing was working. When I got home, I connected it to my Macbook Pro for charging, and it worked. It said the battery was at 60 %, and basically confirmed that the iPhone wasn't dead after all.

What is going on? Can someone please help me with this.. do I need a new battery?