If by snuffles, you mean Pasteurella is depends. I guess Around 80% of rabbits test positive by Pastuerella now, but not all are “sick” from it if that makes sense. They have it in their system but they are “immune” to it. Pasteurella is highly contagious though, and can be spread by the handler’s(you) clothing/skin or by sneeze particles floating through the air or sharing toys ect.. It’s kinda a roll of the dice on what could happen! Each rabbit is unique, and it’s very hard to tell how it is going to react with the bacteria present.
The bunny you are fostering could have either been in contact with a sick bun, or his mother could have had Pastuerella. A mother rabbit (even if not sick from it) can and will most likely pass the infection onto her kits. And being on 5 weeks old, the stress from moving, being away from mom at such a young age ect. could have been enough to make him be actually sick from it.
Here is an interesting/informational article about Pastuerella- http://www.celebratingrabbits.com/stories/pasteurella.html
My rabbit has been sneezing and we’ve tested her for Pastuerella, but we still aren’t 100% sure that is what is making her sneeze.
Good luck, and I hope I helped a little bit!