iPhone 5 won't turn on

Help! I used my iPhone 5 last night just before going to bed. This morning I went to use it and I got the battery symbol to charge it. I plugged it in and I am unable to get it to turn on even after letting it charge for hours. The advice from the Apple store was to wipe it to further seek the problem to fix but I have information on there that I need to retrieve prior to the wipe but do not know how to access it/save it without being able to turn it on. Any assistance is very much appreciated.

Thank you so much!