Fine In Theory
What you're specifically proposing is fine in theory, but in my experience it's of limited utility and much harder to pull off in practice than you might think.
But I want to be clear this is a specific reaction to your "Five minutes as a teaser," idea, and the big difficulty is the amount of time. Five minutes is just not, in my opinion, enough time to establish much of anything. I don't think it's enough to establish much of anything beyond the basics of a background, and it's going to be very hard to establish a real sense of personality in that time, because in RPGs, personality is established through interactions with the NPCs/world and through meaningful choices.
Can you, in five minutes, establish a character's background, establish some NPCs, set up a meaningful decision, and let them make and act on that decision?
Maybe. It's not impossible.
Can you do it four or five times in a row in the same session, without scripting? I'm skeptical.
Can you do that in a way that all puts them in the same scene together at the end? Now I'm really skeptical.
I've done things like this in table top RPGs, but very sparingly and only in nearly optimal conditions, like, "This PC has amnesia, and therefore no real backstory, and is going to crash onstage at the start of the game." And it still took me more than five minutes with that player.
The Tension Of The Clock
The tension of the clock is what you're really fighting, here, because the next thought for me would be, "Well... okay, more than five minutes then." But here's the thing-- that extra time gets multiplied by the number of PCs you have in your game. If you need half an hour each and you have four players, you've talked yourself into a session where all the players have a half an hour of inactivity at the beginning.
And God help you if the third player does something weird and unanticipated that keeps you from smoothly weaving all the players into the same scene at the end of them. If you're not pre-scripting the scene, that's a very real risk. And if you are, then... why are you playing through it?
It's not a bad idea in theory. But my experience is that, the way you've proposed it, the clock will be pulling you in opposite directions.
Adjacent ideas that I've tried or been part of include:
Running special one-shot mini adventures for players before the game starts. Took me about 2-3 hours each player (this was when we all had oceans of free time) and it loosened a lot of the constraints. But it didn't fulfill what I think you want the most-- establishing each PC in the minds of the other players. It only served to let the player develop the PC a little bit before the main game.
In the context of e-mail games (i.e., not 5e at all) I've found that starting the players off separately, in their own e-mail threads, can work very well. The benefit here is that, when I run e-mail games, everyone can read everyone else's thread, and they can run concurrently. Pacing and agency can still be a bit of a problem, but I've been doing this a long time and I'm confident of my ability to weave things together when I'm not on a deadline. But this is not 5e.