mathman has hit it on the nose.
Very few rifles are accurate enough to group 5 shots as tightly as 3 shots. Even 5-shot groups from benchrest rifles will "open up" a little over 3-shot groups, purely because of the laws of chance.
If you shoot enough shots in a group, the group's diameter will eventually include just about every shot. This is why I test prairie dog rifles with 10-shot groups. Even though the diameter of a 10-shot group doesn't impress many of today's shooters (3/4" is really good) it tells a hell of a lot more about a rifle's accuracy than a 3-shot or even 5-shot group, especially with a hot barrel. And hot barrels are the norm in PD shooting.
One reason 3-shot groups are so popular these days is the chance for a tiny group is so much greater with fewer shots. Then when we shoot one of those semi-accidental one-hole 3-shot groups with our factory rifle we can post it on the Campfire.
This doesn't mean some rifles won't consistently group 3 shots with all the bullet holes touching. Many will, even some factory rifles. I even own a Ruger No. 1 .25-06 that will do it with 75-grain Hornady V-Maxes. But if I shoot a 5-shot group with the same load it's bigger, even if I let the barrel cool down, due to statistical probability.
