My Iphone 5 Is Charging But Not Turning On. Test Your Charger And Lightning Cable. Otherwise there is a chance the battery may have gone faulty.

If the charging port is damaged your device probably needs service. When the device is in DFU or Recovery mode it will automatically get detected by the software. Just keeps showing low battery.
Let your device charge for a half hour.
If your device is still unresponsive force restart your device. Press and hold both the side button and the volume down button until you see the Apple logo. If your device is still unresponsive force restart your device. Remove any debris from the charging port on the bottom of your device then firmly plug your charging cable into your device.
