Chosen Solution

Got an iPhone 5 for display assembly repair. It also needed a new lightning dock, and power button. I replaced all three of those part, but the power button still won’t work. A little confused as to why. It didn’t appear as though the phone had been worked on, prior to me getting it

If a confirmed known good power-mute-volume cable does not solve it, you probably have an issue with one of the components behind the SIM tray as already pointed out by @corklad or some other filter for that function, usually next to the power-mute-volume flat cable connector on the board. In both cases you’ll need micro soldering tools to fix it.

have you checked at the back of the sim tray for any damaged components?