My iPhone 5 power button stopped working. I took it to the Apple store and to AT&T and neither could help in fixing it. The Apple store actually recommended iFixIt.com
Great. It was more involved than I thought it would be but it was easy to do. Though there is obviously something else wrong with the power button because the new one doesn't work either.
Make sure you get the Pentalobe Screwdriver as well. It's not listed on the tools needed, but they mention it in the video and you do need it.
iPhone 5 Power and Lock Button
Phillips #00 Screwdriver
Small Suction Cup
SIM Card Eject Tool