Edit: This post has been heavily modified for clarity.
Firstly let me state. We actually have someone in our guild with 5 on a single character, but, he had 3 before the "Yea we screwed up one of the biggest 'self-worth' systems in Legion, sorrynotsorry" hotfix.
However out of all the people I know, in all the guilds I have contact with, no one else has heard of anyone with 5/5+ in their social circles.
If we look at http://www.wowprogress.com/character...vencrest/Cerli the guy with the 2nd most AP in the World, and 1200 M+ to his name, he also has 4 on a single character.
Blizzard has insisted multiple times there's not a cap, which leads me to believe their justification for saying such is perhaps there's a softcap (which is vastly different), with diminishing chances/diminishing bad luck protection.
If you could research all of WoW there would be three questions.
a) On average how much legendary chance content did it take people to go from 2-3 on a single character.
b) On average how much legendary chance content did it take people to go from 3-4 on a single character.
c) On average how much legendary chance content did it take people to go from 4-5 on a single character.
My hypothesis is that a) and b) would be similar, and c) is much much much greater.
I am not saying you can't have 4+, I am saying it is far harder getting your 5th than it is getting your 4th.