General heuristics that change:
Combat is slowed down. Instead of everyone at the table, everyone is at the table at different times. This means that an encounter of just 2 or 3 turns can take 2 or 3 weeks possibly. This has some minor advantages as well, since people have time to react.
Role-playing has more time for enrichment, generally. If someone wants to write a page about how their character perceives their current circumstances... this costs almost nothing in terms of game time. It's a lot easier to write a quantity of quality text in twenty minutes before you post it than it is to spend 20 minutes at a real-life table game.
Complicated inputs are more difficult, like reacting to spells/abilities/events... it's not real time like a face to face game. You end up with if x, then y, then z. For example, you could want to move, attack, and if you kill your target move some more. That's at least 2 posts in PbP which could be delayed by a day or more depending on how free people are to pay attention to the game.
I also feel like long term PbP is even harder than a real-life campaign. They are both hard. People have things come up. We all do. But PbP often collapses... or at a minimum some percentage of people leave... because of life reasons. This has happened to me a dozen times. I'm older and wiser and more respectful of other peoples time and more aware of my own time constraints at this point than I was... my god... 15 years ago... but it is what it is.
5th edition is easier than 3rd or 4th, in my opinion. The rules are faster and looser. The general level of knowledge about the game is higher. It works pretty-good honestly. Of-course, what's really good for PbP as a medium might not be what's best for the game. I'm still learning 5e.
There are metagame changes that might be helped by adaptations I am not yet 100% aware of. For example, since combat takes X more time, smaller more focused combats might be better. My last couple fights have been slogs of sorts. I think me and my players are fine with them in this context, but... as a thought... it might be better to have shorter higher damage lower hit point enemies just to sort of focus the game and get past the "slow" combat and back to the relatively efficient role-play part of the game? I am not 100% certain on that. It's just a thought.
I think the best advice I can think of is to be very open with yourself about trial and error. Start up your game, get your players and your campaign going. Get started. See what works and what doesn't work. Be willing to make changes. Communicate with people playing what you think. Hopefully they communicate back. This medium is NOT exactly what the game designers expected. It's stronger in some places and weaker in others. I'd say just keep an open mind.
If we were talking about something I ran a dozen times like 3e or 3.5, I could pick nuances out... but really... I'm still pretty new to 5e. I'm still learning fundamental things.
