You can also check on Apples site to see if your iPhone 5 qualifies for the power button replacement program. You put your serial number in, and it will tell you if that particular phone is eligible for a FREE button replacement. So that would be better than taking it to some dodgy backstreet phone repairer. I know, as mines in at the minute getting replaced, and as a bonus, they will swap your battery too at the same time. so according to the invoice I'm getting a new power button and battery for nowt. Not bad customer support for a 3 year old phone is it? Amazing actually springs to mind.
And as a bonus, they will loan you a phone to be going on with, as it takes about 5 days to do the repair.