5-6 hours is doable, and definitely sounds like a better option than leaving him at home for a week if there is nobody to care for him. Do you have a carrier? Be sure to line the bottom with a towel or mat, so that he won’t be slipping and sliding around inside when the car moves (and to soak up any pee). Definitely try to secure the carrier as well, so that it doesn’t go flying if you need to make any unexpected sudden stops. Most bunnies won’t really be interested in eating or drinking anything during the trip, so personally I like to give my bunnies a heaping pile of wet veggies before leaving, to make sure that they’re hydrated. Adding a handful of hay to the carrier is nice too, although it’s possible that he won’t touch it at all.
Just to keep options open, are you familiar with the rabbit rescues in your area? I’m pretty sure there are a few in Southern California, and oftentimes many of them will board bunnies for a daily fee, if you find that to be a better option.