Chosen Solution
I drop my phone and now it wont turn on The red battery without plug appears but the charger is connected The apple logo will appear for a while then a dim light will follow and it stays like that for some minutes What is the problem? And how do I fix it?
First what I would do is try a new display and battery. They both could have taken some damage during the fall. If that doesn’t work it might have damaged a part of the logic board. Open up the phone and check for corrosion and try reconnecting the connectors. Fixing the iPhone Display: iPhone 5 Screen Replacement Fixing the iPhone battery: How to replace your iPhone 5 battery