I recently moved 12 hours with my two.
Now I was lucky that my rabbits had each other as a comfort.
My girl is a nervous traveller. The times I haf to travel alone with her I left her stuffed animal friend in her carrier so she could cuddle into it.
For me the plan was to make sure the buns ate before we left, I always try to get them to eat greens that have been soaked in water – this way i know theyve eaten, and have had water.
My guys have done the five hours trip plenty of times. For us I always give them a break at about the halfway point, where I offer them their favourite treats and a bowl of water. I usually look for a quiet grassy area that is safe, and I let my buns out to stretch their legs, nibble the grass and maybe eat.
Because its only a five hour trip, it is not vital for your bunny to eat on the trip.
I usually make sure their set up is ready before I get it there. If you cant organise that, be sure to bring all his normal food (I even bring a large bottle of water from home so that doesnt taste different)
Blankets that smell of home, favourite hides etc can help a rabbit to feel more at ease.
I always put a blanket on the enclosure so that they cant see too much of their new home and therefore cannot stress.
Keep an eye out for signs of shock, have a list of possible vets you can get a hold of as you travel, and have a little stache of critical care on hand in case your rabbit is struggling to settle.
I was also prescribed a natural calmer, called nutra calm. Perfectly safe for bunnies and just takes the edge off of fear.
For a once off journey, this isn’t that huge, though it is unpleasant for him, they do settle well, my two were completely over their ordeal after a day of napping and eating.
Good luck!