I was given a used iPhone 5 and the battery was definitely sub-par. It did not hold a charge for very long, and oftentimes it would drop from 30% to dead.
I was extremely hesitant to tackle this on my own. After I saw how much Apple wanted for a replacement I decided to give this a go. I'm a poor college student, so I can't afford a brand new iPhone-- so I was extremely cautious. I watched the video and read the reviews beforehand and it wasn't too bad. The hardest part was prying the screen off. If you're on the fence, go for it-- you've got this!
Use a magnet to hold on to those tiny screws. I completely skipped the step with removing the screen. The way I see it, the less I tinker with things the less chance there is for things to get broken. So I just held it screen at about 85 degrees with my left pinky finger while I removed and replaced the battery. If you need to set the screen down for some reason that's not a big deal. Also, when you're putting the screen back in place, make sure to start with the top of the screen first. I just tried to evenly press it all down and the top was still sticking out a little. So I pulled the screen back up and started at the top and now it's as good as new. My battery first booted up with 68%.