Screen replacement.
It might have damaged the LCD, so you may need to get that replaced as well. Screen replacements are relatively easy, they're cheap on EBay and since it's a 5, you don't need to worry about the Touch ID cable. You'd need to transfer the home button.
The iPhone screen is made of layers. Underneath the glass is the Liquid Crystal Display, which is responsible to for the touch and the display of images.
To know if your LCD is broken, there would be out-of-place lines, blurry or black spots or a black screen.
Only do a screen replacement if you know how.
Anyone please correct me if I'm wrong.
I don't think that it's a quick fix by pressing a few buttons, but you should definitely take it into an Apple Store or third-party repair shop. (Usually cheaper)