The broken front screen is a hardware issue and can easily be replaced. Replacing a screen is simple and will take hardly more than a few minutes, possibly less than 15, if you follow all the steps correctly.
I highly recommend that you do it yourself, as it is a great learning experience and can help you, your family, and friends save on high labor costs. The tools we would need to carry out the procedure include a non-conductive skewer, a pentalobe screwdriver, a Phillips screwdriver, and an optional separating blade. Of course, you will also need the replacement screen.
You can buy these components separately and easily; however, if you purchase them individually, you may be charged extra for shipping. Therefore, I recommend buying an all-in-one kit that includes the tools and the replacement screen.
iPhone 5s Screen Replacement Kit
iPhone 5s Screen Replacement with White Screen
iPhone 5s Screen Replacement with BLACK Screen
iPhone 5s Screen Replacement Procedure
1. Using a Pentalobe screwdriver, unscrew the two screws located on the left and right sides of the charging port of the iPhone 5s.
2. Gently lift the screen using a non-conductive skewer or separating blade. Avoid using excessive force to separate it, and do not lift it too high.
3. Detach the home button cable connected from the screen to the main board, using a separating blade or non-conductive skewer.
4. Since you can lift your screen to 90°, a metal plate acts as a cover for the four cables of the camera/speaker attached to the main board. Open the four screws using a Pentalobe screwdriver.
5. Gently detach the three flex cables connected to the main board using a non-conductive skewer.
6. Now that the screen is separated from the phone, remove the speaker/camera at the top of the screen by unscrewing the screws holding the metal plate over the cable.
7. Unscrew the screws from the metal plate covering the home button, using a Phillips screwdriver.
8. Also, separate the large metal plate in the middle of the screen by unscrewing the two screws on both the left and right sides.
9. Use a non-conductive skewer or a separating blade to detach the cables of the camera/speaker and home button, then place them aside from the old screen.
Now, a bit of reverse engineering.
10. Place your camera/speaker in the spot designated for the new screen, and also position the home button, attaching the cables to the screen.
11. Attach the metal plates to the camera/speaker and home button and the large central metal plate on the screen, just as we previously removed them, using a Phillips screwdriver.
12. Attach the three flex cables of the new screen to the main board of the iPhone 5S. You can use your fingers to plug the three flex cables into the main board.
13. With the help of a Phillips screwdriver, secure the four screws over the three attached flex cables.
14. Press the new screen onto the phone and use a pentalobe screwdriver to tighten the two screws on the left and right sides of the charging port. Now turn on your device with the new screen; it should work.