A dream sequence wouldn't make a lot of sense to start Episode 6 given it wasn't nighttime at the end of Episode 5 and we hadn't even worked out where the MC would be sleeping. Plus, and I feel I need to emphasize this, dream sequences in BaDIK suck.
How would that be in any way preferable to an equal length session of actual DnG in the middle of Episode 6 that lets us see the actual characters interacting with each other in a novel setting?
Here's the beauty of fictional writing; you can make anything make sense.
We don't necessarily have to pick up the story right where it left off in ep 5. Yes, every episode has done that so far, but it doesn't mean that DPC has to stick to that formula. We saw the MC get his jacket and standing in his new room at the end of ep 5, right? Well, what if he spends the night there on a spare mattress or in a sleeping bag? That would solve the issue of where he sleeps and wouldn't have to have different renders for different places based on previous player choices.
It's not something we necessarily need to see or have explained either because you don't always have to show everything that goes on. It's like with TV shows where the start of the next episode is days after the previous one ended because nothing particularly significant happened in the story during that time, and so the next episode just picks things up at the next major story beat.
But generally you do need to fill in that gap with something, like a flashback, or a scene with side characters, or a dream sequence. In the case of the latter, seeing the MC dream about 3 LIs in a fantasy environment he has recently become aware of would make sense as it's something that's very fresh in his mind and it could give an insight into his thoughts and possible concerns about recents events, which have been tumultuous to say the least.
Another option besides a dream sequence bridging the gap between eps 5 & 6 could be that we see Quinn going to meet her dealers on Sunday night at the beginning of the episode before we see the MC wake up in the DIK mansion the next day. Either one of these things can work in the context of this story and even if that isn't how it will be, there's nothing to say that either one couldn't be a possibility.