Not able to charge iPhone 5
Some iPhone 5 are eligible for a free battery replacement. Maybe that is related to your issue?


  Apple has determined that a very small percentage of iPhone 5 devices
  may suddenly experience shorter battery life or need to be charged
  more frequently. The affected iPhone 5 devices were sold between
  September 2012 and January 2013 and fall within a limited serial
  number range.


You can test if your phone is eligible, on this website.