Do a reset, by holding the Home button together with Screen Lock. Only release when you see the Apple logo reappear.
Afterwards, as bizarre as it sounds, users reported that after using some of the control centre features (flashlight and camera) when the phone is locked, was the cause. IPhone 5 in iOS7 flashlight and camera not working You will see that several people have reported that opening up the camera app, toggling HDR on and off, flash on and off, seemed to have fixed it. Good luck.