The problem could be as simple as either rebooting the iPhone or opening the iPhone and reconnecting both the LCD and digitizer connectors since in some situations it can become loose after dropping the phone.
You will need a pentalobe screwdriver, #00 philips screwdriver, plastic spudger, and a suction cup (or iSlack tool) to open the iPhone and diagnose the problem. There are guides on here for the 5S that will greatly assist you with opening the iPhone.
Open up the iPhone, being careful with the touch id sensor flex cable, disconnect the battery, and then remove the metal shield that covers the screen connectors and take a look at the connectors. Remove and reconnect them and see if that solved the problem. Lemme know if you need help or more info.
Best of luck.