Hi there,
This youtube video might help you: https://www.youtube.com/watch?v=nJCZJwrklHs
In which he opens the phone up, cleans all the sockets that attach the screen to the motherboard with a toothbrush, and then secures the cables back into their sockets.
Note that he is working on a 5s, in order to open a 5 you can follow this guide, which is essentially the same but without the booby trapped cable connected to the home button that you will see in the video.
[guide|10588]
Hope this helps!