This took some research to figure out, so I’m sharing it and keeping it here for future reference.
Version used: GoPro HERO5 Black update v01.20
Download the latest update for your GoPro Hero5 Black here: https://gopro.com/update/hero5
To take the highest-quality (RAW) photos with a GoPro Hero5 Black, you need to enter photo mode, set FOV (field of view) to wide, turn Pro-Tune off, turn WDR (wide dynamic range) off. Details and photos for these steps are outlined below.
Press the Mode button (right side of the GoPro)
If not in Photo mode, press Mode button again until the screen says “PHOTO”.
If the “FOV” at the bottom right of the screen is anything but “Wide”, then tap it and slide the options up or down to change it to Wide. Tap it and make sure “Wide” is blue.
While in Photo mode, swipe your finger from the right side of the screen to the left.
The screen that appears after swiping has three pages of settings. You can swipe from right to left again to see the additional pages.
If PROTUNE is on, the first page will show Color, WB (White Balance), ISO Min (minimum sensor sensitivity), ISO Max (maximum sensor sensitivity), EV Comp (Exposure Compensation), Sharp (Sharpness Level) and ProTune Reset. Tap the power icon () at the bottom of the screen to turn PROTUNE off.
With Protune off, you can swipe to the right to turn off WDR (if needed).
Swipe to the third page, “RAW FORMAT”. Tap the power button icon at the bottom of the screen to toggle RAW mode on and off.