I just completed a successful iPhone 5 battery replacement. Thanks iFixit.
One hint: If you get the dreaded white stripes due to a loose LCD cable connector, as discussed in Step 15, don’t just remove the cable cover and press on the connectors. Pry up the connectors completely and reseat them.
I still can’t believe that I didn’t blow up that incredibly swollen battery when I applied the hairdryer to the back of the case. I wish you could have seen the Apple store tech’s face when I brought it in for disposal.