it is a spin-off from "Jackass!"(and that's mentioned a lot in the comments), but there you can only get to know how they've met and their background a bit. everything else what you're asking about was literally explained in this one......
they didn't break up per se, in the past the older guy was pursuing miyoshi and they were seeing each other but not like a couple. more like hanging out with an intention of romance in the future. they didn't even hold hands at the moment and yet hosaka kinda confessed, asked miyoshi to move in with him after graduation and gave him the keys, which made miyoshi happy and _scared_ at the same time. so he ghosted hosaka, but not for MANY YEARS lol, literally 8 months passed. he took the keys tho, so he had no problem getting into apartment and for the adress I assume he knew it already, they were close enough. miyoshi was not dropping by during these 8 months, but started in the present after they reunited and started talking again. if you read it properly, you would've seen that it was hosaka who drugged miyoshi to his workplace and invited again after, the reason is painfully obvious - he wants them to get together. as for the guy in ch5 I have no idea, it's a new character, so we'll see later on if he's hosaka's ex (I'm also guessing he is).
this manga has it's own questionable and problematic moments, but I didn't see any gaps, feels like we've read different stories. if you're reading scarlet beriko, it's important to pay attention to every panel and not just scroll through it. and not everything has to be on-screen, it's up to mangaka to decide what they want to focus on.
I hope this answers your questions
Is it missing some pages or is it continuation of another manga?? Like why did they break up? How did he know about his house? How come he keeps dropping by even though he left him for many years? And now a guy drops by which I'm guessing it's the older guy ex or the rival!!