The missus has an iPhone 5 that wasn't holding a charge very long. Ordered the iPhone 5 Battery Replacement Kit from iFixIt because you all produced such helpful videos online.
The repair was really simple. The kit had all the necessary parts for the repair, and the only challenge during the job was getting a good enough seal between the chunky suction cup and the screen. That was remedied by slightly dampening the suction cup.
Issue after the repair: After the repair, the phone turned on without any problem, but we noticed a yellow area near the top of the screen over to the right. From what I've read, this is probably caused by something underneath pushing up on the screen. It's probably the shield covering the screen connectors, so I'm going to try loosening the screws on that a little and trying to get it to seat a little better.
Slightly dampen the suction cup to get it to seal on the screen a little better.