My battery has been terrible for the last year. Recently it's been dying suddenly when it's said 20% life left. I've been tethered to the wall when doing anything on my iPhone 5, other than just reading websites.
Went pretty dang good. The battery is really stuck in there. I thought the prying tool had too much give in it and seemed to bend too much to where I lost leverage. Prying from the top seemed to work best.
I did try to just prop the screen against a big book so I wouldn't have to take it apart. That worked okay until I tried to pry the battery loose. I really didn't trust the two side pry locations. The one closest to the battery connector worried me with the real narrow ribbon cable running along the side. I went ahead and remove the display, so I could pry the battery loose from the top. It went fine after that.
Look carefully at how the cover plate for the display cables lies. I didn't and it took to bit to figure out if the inside edge of the cover, closest to the battery, was to the left or right of the edge/ridge that would be under the cover, when it's in place. I put it over or to the right of the edge/ridge and the screws lined up fine.