Well no, by their definition, if he consumed five or more drinks he wouldn't be a heavy drinker, he would have heavily drank. There is a meaningful distinction. The next sentence, as you'll have seen, is :

SAMHSA defines heavy alcohol use as binge drinking on five or more days in the past month.

And at that point, I totally agree. If someone is drinking more than this person, and on a regular basis, they would certainly seem to have a problem.

They are definitely not saying if you drink five beers one day you are now an alcoholic.

that's affirming. i had an ex that would house the better part of a sixer of 9-12% ABV cans every evening. i am not really one to scrutinize, but i noticed it after a week and thought, "isn't that kind of a lot?" very costly $$, but also like damn. we were the same age, but i had 100 lbs on them, and that would have given me the spins. i dismissed it at the time as most of my life ive been a "lightweight" with limited tolerance and i quit altogether 7-8 years ago.

to see something fairly objective that isn't distorted by an experienced drinker's ability to appear functional is eye opening.