iPhone 5 Lightning Connector and Headphone Jack
Be very careful here, at this point the phone power is live! a slip of the connectors or a loose screw could let the magic smoke out of the chips (chips won't work without their magic smoke, you know :-)
I'd disconnect the battery before messing with the connectors.
After re-assembly of the phone you need to do a full power reboot, hold down both buttons for about 30 seconds until the apple logo comes up. This is specially true if you follow the instructions and reconnect the battery before the display. The chips on the display won't get initialized if the display is not connected when the battery is plugged in.
Rule #1 on electronics repair methodology: to prevent damage to the electronics, power should be the first thing to be removed and the last to be restored. I'd disconnect the battery before touching anything else, a slip of the screwdriver or a loose screw could cause a fatal short circuit.
Make sure to clean any bits of golden glue left on the phone case
This step completely ignores the microphone rubber boot (the black thing left of the headphone jack) Without it the microphone will not work right, it will still get your voice but it won't be as clear as before.
The original mic has a bit of glue holding it into the boot, the replacement part does not have any double-sided tape there so it's tricky to keep it in place when mounting the assembly back. I'd not advice trying to glue it down, if you get any glue on the mic port (the small hole on the bottom) you are toast.
I have a problem with this instructions not showing the re-assembly of the phone. There are specific sequences and cable routings that must be done right. For example, don't do step 31 until after 28 to prevent damage to the flex cable.
Also, to prevent damage to the phone electronics the battery should be the first connector to get disconnected and the last one to be put back. There also no mention of ESD prevention or control, a $5 wrist strap could save you from blowing up your $700 phone.