I have provided the facts. Those facts are clear and absolute. So far everyone who has disagreed has fabricated things out of thin air in order to try and be right. It's on you guys to prove those fabrications.
Oh, it's
facts you're a wanting? OK. I'm game!
A 5e character with a 5 INT can choose any Background. Including "intellectual" backgrounds like Sage.
A 5e character with a 5 INT can go to college for lore and become a Lore Bard. By 3rd level they'll have a total of
8 skills. They can even be good at them! (if their player avoids INT-based skills, of which, as I like pointing out, Medicine is not ) Or they can be barely competent at 2 INT-based skills if you compensate using Expertise.
A 5e character with a 5 INT can become a
wizard! Put that in your pipe-weed pipe & smoke it. Their spell attacks rolls & save DCs will be bad. That's all. An INT 5 PC can conceivably learn 9th level spells -- there's no INT restriction at all. In fact, it shouldn't be
too hard to design a
playable INT 5 wizard by selecting mainly utility spells which don't depend on spell attack rolls or saves. So stick to things like divination, summoning, animating household objects & the dead, and... gasp...
teleporting (which requires "familiarity", but no INT check).
So how do you reconcile this? You're claiming a 5 INT is barely smart enough to have a
class in the first place. The rules claim, or rather state, a 5 INT PC can have
any class (and theoretically learn the most complex wizard-y spells). Heck, if I have time I might work up a playable 5 INT wizard, "Herp Derp the Eye-Fighter" (he likes to fight Beholders... because he is an idiot!).
To be clear, I'm not saying a 5 INT PC should be played the same way a 15 or 20 INT PC is. But if an INT PC isn't prohibited from learning 9th level wizard spells, then they shouldn't be frowned upon for voicing a
smart idea or
solving a riddle during a session.