iPhone 5 sound not playing through headphones I have tried multiple working pairs of headphones (tested on other devices) and the iPhone doesn't play any sound through headphones.
If the problem persists, you may have a whole different problem on your hands. Basically, dust can get into the earpod jack and cause an electrical disruption. To fix this, put the earpod plug in the jack until you hear the click, and then pull it out again. Do this over and over again. 
   Try it out, and if you have sound, then you have fixed it. If this has not happened yet, it will most likely happen in the near future, so be prepared. (it happens to some apple devices after a while).