There are a number of ways to zero a pistol and all will tell you its depends on the needs.
First off, anything within 5 yards you can bet, best practice if it is decleared a threat and time is against you, just simply draw the weapon and point center mass on your target, you are bascially guarenteed to hit vital areas.
Zeroing a pistol is meant for targets beyond 5 yards and ensuring accuracy.
Problem is a bullet does not fly in a straight line. So lets look at various, effective-fire ranges for the average shooter with a handgun.
Common zeros are, 5 yds ; 10yds; 12yds ; 15yds.
Uncommon and what we will argue is the better zero; 25yds.
we will add our documented personal testing, but I have been zeroing this way for a while. Below are some pics completed with great documentation provided by NRA shooting illistarted. ( Best Distance to Zero a Pistol-Mounted Red Dot | An Official Journal Of The NRA (shootingillustrated.com)
We will follow up with some additional zeroing ranges for the pistol, but in a nutshell the 25yard zero is the way to go with a handgun.
Tip: your 25 yard zero does not need to be a very tight grouping, within a couple inches or so.