Two Battery Replacements, One Careful and the Other, Quick
The batteries in two iPhone 5 phones were discharging rapidly.
Not knowing exactly what to expect, I carefully followed the instructions and successfully replaced the battery in the first of two phones. While it was somewhat intimidating to pry off the screen, all went well. The tools provided in the repair kit made this task easy. I used a hair dryer set to low to help dislodge the old battery.
After buttoning everything up, the phone would not boot, but after again removing the screen (but this time holding the screen vertically by affixing it to a [yes!] Snapple bottle with a rubber band), I discovered that the battery connector was not properly seated on its socket. Again closing things up, the phone booted up normally, after which, as instructed, I conditioned the new battery.
For the second phone, I realized I did not really need to disconnect any cables except for the battery connector. I again propped up the screen vertically, but this time ignored all the cables connecting the screen to the case. Once again, a little gentle heat was necessary to help dislodge the old battery. This time, the connector seated correctly and the phone booted immediately. The second repair took about 5 minutes.
Both phones now hold their charges significantly longer than they used to.
See my repair experience above. No need to be intimidated; it's pretty straightforward.