My iPhone 5 battery was behaving very oddly. It would drop suddenly from say 58% to 17% then shut off completely. When I plugged it in it would jump from say 17% to 35% instantly. I got tired of having to recharge it constantly and after reading lots of advice on making battery life better decided maybe the battery just was nearing end-of-life.
Not terribly difficult. I read the repair guide (including the user comments) before I started. Since I also have an iPad, I was able to keep the guide open on the iPad while performing the repair on my iPhone.
1. Removing the front cover was an adventure. I found it very difficult to pry it open, but eventually succeeded. Be careful when opening the cover not to break any cables. It's just hard to keep hold of the case because it's so smooth. There is a tool with two suction cups (iSclack) that would make it much easier though I wasn't aware of it until after I'd done the replacement and it's $25, so I didn't have one.
2. The only other hard part was removing the battery itself. I found that the suggestion to use a hair dryer to soften the glue was invaluable. Just do it if the battery doesn't come out easily. Don't waste a lot of time and effort trying to pry the battery out before heating the case from underneath.
3. When I removed the battery connector cover, the connector came along for the ride. Not a problem, but don't be surprised if it happens to you! Just pull the cover off the connector after you have the battery out.
4. I found that it was unnecessary to remove the front cover completely. Not only are these extra steps, they're extra opportunities to screw things up, so I decided to try just holding the case open at about 80 degrees while working on the battery.
5. The guide and video contradict each other about where to pry when removing the battery. Some of the locations in the video seem downright dangerous. There are breakable things under the top of the battery, for example. One of the comments said to pry from the edge of the case about an inch below the volume buttons. Since there's a nice gap there and nothing to break there, that advice seemed good, so I followed it. Worked great. Once I'd softened up the glue I think I also used the pull tab to lift the other side of the battery without prying on that side at all.
6. Notice how the battery cable (leading to the connector) is folded when you take out the old battery. You'll find it easier to install the new battery if you make similar (gentle) folds in the new battery cable before installing it.