Changing my iPhone 5 battery was surprisingly easy.

I didn't need to pry open the screen. I just pulled with the suction cup and was able to open the whole screen in 30 seconds!

I heated the back (to loosen the glue) BEFORE opening the screen, maybe this is what made the screen removal easier. (dilated metallic rear case?)

Then I didn't fully remove the screen but attached it to a mug as advised by others.

I heated again the case to loosen the glue and was able to remove the battery by pulling on the plastic tap.