I had this same exact problem on my 4s and found the solution was that the replacement LED was not compatible with my older iOS (video solution found here http://www.youtube.com/watch?v=pOr-bHnu0ag). Once I upgraded to the newest iOS (through iTunes since I obviously couldn't do this directly from my phone), the new LCD started working. Obviously, your situation is different since you're on the iPhone 5, but maybe worth a shot.