3-shots only establishes a
point of aim on paper. Tyros, lazy shooters, and the overly cheap think 3-shots is 'good 'nough' to be called a 'group.'
It's not.
5-shots is a baseline group - more commonly a string or sequence of three or four of them (with time between for barrel cooling) - and is necessary to reliably vet the accuracy of a
particular load (factory or handload) in a
particular rifle. Change the load, or switch to another the rifle even using the same load, and you'll have to start all-over.
This pertains to 'hunting'-grade rifles, not precision or bench-rest rifles. For those rifles, a 10-shot string is often used to establish accuracy, because from the git-go they've been set up with tuned and blue-printed actions, Match-grade barrels, and high-end triggers set especially light.
Don't expect much. Most of that stuff is 'junk' ammo. Good as 'range only' blasting ammo but not much else.
The high-grade .223 Match stuff is what you need if you really want to vet your rifle's accuracy potential - especially if shooting a 10-shot 'precision' group.