If I have Int 5 and training in Medicine, and you have Int 10 but do not have training in medicine, which of us knows more about medicine?
Accidental trick question - it depends what level you are. Once your proficiency bonus gets high enough, you might be a thick encyclopedia of specific facts, albeit with no real way to put those facts together, except in that you might have rote-memorized procedures. You still won't be anywhere near as good at them as a normal person who'd done the same, let alone a smart person. Even a normal person could probably give better advice than you though, initially because you'd be spewing piles of irrelevant medical facts.
INT 5 is basically "talking animal and not the bright kind" INT so RPing it differently is pretty crappy. You're literally dumber than a gorilla (INT 6), just with a working voice-box. It's like taking CHA 5 and then assuming your character is totally charming and likeable and memorable and so on, and that just because you can give a speech, your PC can, or STR 5 and testing the DM's patience by carrying around 300lbs of stuff just because this DM doesn't use the encumbrance rules.
Follow-up, how often do you require an ability check to know something? All circumstances? Are there situations where an adventurer can auto-succeed? Auto-fail?
At my table, taking a knowledge skill confers knowledge AND grants a bonus when checks are made. I do not require checks in every case.
Could our handling of checks explain some of the difference in our positions?
The suggestion was that you can 100% avoid making INT-skill checks to know things. Not that you can't know some stuff due to your training and background - but that you can 100% (or very close) avoid INT-skill checks, and didn't even have to check with the DM whether your PC knew stuff, you could just come out with stuff and it would somehow be accurate.
Identifying unusual stuff is a situation where I'd almost always call for a roll, unless the character had a very specific background that meant they just knew (which does happen, but not routinely). If someone had Expertise in a skill, I'd probably give them a bit more leeway in what I considered them to "auto-know".
But we're talking about what Sherlock Holmes does, which is to merrily prance into a room, look around it basically once, and start making actual declamations/proclamations about stuff. That's definitely going to need a check or three.
If someone wants to take INT 5 and somehow contrive to get Expertise in a bunch of knowledge skills, and has a consistent and sufficiently plausible background for the character, they could avoid more rolls than most, but you don't get to be Sherlock Holmes if you don't make any checks, especially not whilst being demonstrably worse at logic, math and so on than a gorilla. You get to be Lestrade, maybe, on a good day.
I mean, that's the big issue here - to be truly imaginative about real-world (to your PC) situations, you need to be intelligent. You need to understand how things work. Intuition alone isn't good enough. Intuition is what gets you thinking "Hmmm this scene doesn't seem right, it seems staged" and maybe that's WIS (arguable), but INT is what lets you actually understand what happens in an A-B-C way, and most of the skill needed to identify unusual things found at a scene are likely to be INT skills.
To use a media example, think of the Robert Downey Junior Sherlock Holmes movies, where he can basically replay what happened at a scene because they understand how everything works. Someone with INT 5 could never do that. They don't understand the world well enough. If they have WIS 20 and Insight they might well take a look at a fleeting expression on the face of someone there and know that person knew more than they were say, or even that they did it, but they could never formulate the hypothesis needed to prove that person did it, or even scare that person into a confession, unless just pointing to them and screaming "YOU DID IT!" was good enough.