It's most likely the front camera assembly being at fault from my experience.
Can you confirm that the front camera, earpiece speaker, auto brightness, proximity sensor (when you put the phone near your ear during calls the screen turns off to prevent accidental touching of screen). Also the top microphone which can be tested by putting the phone in speakerphone mode and checking if the caller can hear your voice during speakerphone mode.
All this testing is for the front camera assembly.
If one of those functions do not work properly at all then I recommend replacing the front camera ribbon cable assembly.
Guide to replace the part:
iPhone 5s Front Facing Camera and Sensor Cable Replacement
You can buy the replacement part from iFixit online store:
iPhone 5s/SE Front Camera and Sensor Cable