My iphone 5 has gone blank and does not charge

First try this:

Reset your device: hold down the home button along with the sleep/wake button until you see the Apple, then let go. (No data loss)

Inspect the charging port area for dirt/debris/fluff build-up that may be preventing a good connection and use a wooden toothpick, soft clean toothbrush, or a can of compressed air to clean it. Also look for bent or broken pins. Try another cable and/or charger block (be sure to always use a genuine Apple certified brand) in a known good outlet. If you're using a USB port, try another port. If you're using a hub, try a direct connection. If you're using a USB port in the front of a desktop computer, try one in the back. If all these fail, make an appointment at your nearest Genius Bar to have the device evaluated.