The instructions are designed to do several things. Mac users in particular are notoriously lackadaisical about rebooting. These machines tend to have many 'lid =' open/close and power saver activations and are, in general, in a precarious state most of the time. Additionally, a bad install happens from time to time so the process is designed to get last install off, remove accumulated OS cruft from long between-boot cycles, and in general give software a fighting chance to get a clean installation without other software's interference.
Actually, the 'wait five minutes" line has been in Clean Install Instructions for several years and is not an instruction step for this specific issue. In general, it stems from my days as a Lightroom Consultant who saw too many persons jump to their computer immediately after application launch only to declaim 'its still broken!' without giving Lightroom a chance to fully load, rebuild indices, complete partial syncs, etc. - essentially 'settle down'.
In the 13.x builds, there is an additional component in that AI Models do not install with the initial Creative Cloud App installation. They begin to install after the first app launch. In this case, the '5 minutes' also allows a little time for the models to download.
There's no mystery - my instructions have contained this since at least November 2019.
Don't read too much into '5 minutes'