Good guide, but missing a step. In the one I disassembled, the optical drive needed to be removed (it just slides out), and two screws that were holding in the keyboard needed to be removed before the keyboard would come out.

@Ariel - The blue that you are seeing on the screws is simply leftover loctite compound that is used to prevent the screws from working their way loose during every day use and does not give any indication as to the length of the screw. You should notice that, generally, you have two lengths of screws out of the 4 that came out...2 with longer threads and two with shorter threads. The two with shorter threads need to go in the bottom two holes...these two screws are not exactly the same length (difference of 0.1 mm), but mixing them up should not cause any harm to the phone due to such a small difference. With the two longer ones that are leftover, only one of them will be magnetically attracted to your screwdriver...this is the one that goes in the top left hole. The one that does not easily attract to your screwdriver goes in the top right.

This tutorial will give you all the info you need:

iPhone 5s scherm vervangen

First try a hard reset by holding down both the power button and the home button at the same time for at least 10 seconds. If that doesn't work, get back inside the phone and reseat the connectors. If the problem persists, either you received a bad part, or the part was damaged during installation.