iPhone 5s screen goes black during a phone call
Is your phone in a protective case?  My wife's iPhone does the same thing because her case is loose and slides over the proximity sensor and thinks it's still by her face.  

The screen turns black because of a proximity sensor on the phone. This is to save battery during a call, and to protect the buttons from being pressed when it's up against your face. This feature can not be disabled. The only way I have been able to prevent the screen from turning black during a call is by using a Bluetooth headset, earbuds, or speakerphone during the call, and never bringing it close enough to the face to trigger the sensor.