Speed is not your friend. Much easier than I expected but requires patience.
15 minuten - 1 uur
After about 2 years of hard use and too much time on the charger, my iPhone 5 battery stopped holding a charge. Over about 2 weeks it went very quickly from having an annoyingly short life to being useless. All I needed was a new battery.
Success on the first attempt! The whole process took me about 35 minutes. Disclaimer: I am an electrical engineer with a lot of hands-on electronics experience. But this was the most delicate thing I have ever worked on. You won't believe how tightly things are packed in there!
There were 3 tricky parts: opening the iPhone; dealing with the small and delicate connectors inside; and getting the old battery out. In all cases my worry was out of proportion to the actual outcome. With the provided suction cup and some harder-than-I-liked pulling, the phone came open. Brace your hands as you pull. Mine came apart kind of suddenly and it would have been easy to pull the screen part too far away from the battery part. That could be a disaster for the cables. More on the connectors and battery in the Enlightenment section.
The connectors in the phone are incredibly small and delicate. Take your time. When putting them back, alignment is critical. Do not try to force them in place. I had to play with them for a few minutes (literally 4 or 5 minutes) but once they lined up they connected up just fine and it was pretty clear that they were well seated. There is not a lot of tactile feedback, though. You need good light, maybe a magnifier like I used, and patience. Look from all sides as you line things up. It helps a lot. Use the plastic prying tool, even when putting things back together.
It took some effort to get my old battery loose. The adhesive was doing its job very well. Do not force it. Use steady pressure and move from pry point to pry point. Don't try to get it loose from only one pry point.
Putting everything back together was much easier than taking it apart!
There are tabs at the top of the iPhone 5 screen portion. When re-assembling, put the tab side in first. When you get it right, the end with the home button will pop right in without too much pressure. DON'T FORCE ANYTHING. When properly aligned, things pretty much drop into place.