The battery on my aging iPhone 5s started bulging, which pushed the screen glass out of the case. Rather than 'upgrade' to a new iPhone without a headphone jack, I replaced the battery.
Relatively easy repair - you definitely want to use the kit for this one. I've done other repairs with regular old electronic repair tools lying around the house, but for this one, the combination spudger tools, pentalobe drivers, etc. were really needed. The internal connections on the phone are very small and fragile - having the right tweezers and spudgers were critical.
Getting the battery adhesive out was the trickiest bit - I had moderate luck getting one strip all the way out, the other broke about a quarter of the way in. Apparently, that's not too uncommon, but is very manageable.
If your adhesive sticks, grab and old credit card/shopper card/etc. and go in from the side of the phone, gently, and scrape the adhesive off, focusing on the metal back of the phone rather than the battery bag. If you go a little bit at a time, you can pretty easily separate the battery from the adhesive without bending or tearing anything - be patient!