iPhone 5s Battery
General comment about the screwdriver tips and reassembly: If you get a screw nicely set in place using tweezers and then use the screwdriver, the magnet will probably pull the screw out before you can tighten it. If this is a problem use just the tip (without the handle) to start the screw, then tighten using the handle.
My battery had swollen enough to start pushing the display out. I was concerned that the glass and frame would separate during removal but using the standard suction cup and lots of work with the spludger (two person job) I got the screen out ok. I expected to have to re-attach the glass the the frame before reassembly but it went back together fine. I used a cable tie to avoid yanking the home button cable.