I've seen some threads where RVers have used this machine or one like it and were happy with results knowing that it wouldn't be as good as a full sized washer.
I'm surprised your 5th wheel doesn't have hookups. Most manufacturers provide the hook ups as part of the unit build.
You didn't indicate what type of camping you plan to do. Most RV Parks and Campgrounds with RV sites have laundry facilitites. We find the laundry facilities are usually kept clean and have used them from time to time.
We do have a washer and dryer (stackable) in our 5th wheel and find them to be very convenient.
For boondocking we use a 25 gallon plastic trashcan in our shower. We put two layers of black plastic bags in it. Put the clothes in it and then fill it 1/4 full of hot water and add a small amount of laundry soap. Tie the trash bags in a knot and then put the lid on the trashcan. As we tow the 5th wheel down the road the clothes get sloshed around and when we reach our next destination we rinse out the clothes and hang them up to dry. Works great in a pinch.