I am just seeing this but we have a washer and dryer in our rig and absolutely love the thing. It's a Splendide 2100XC. They ours will wash and dry about 11lbs of clothes and wash 15lbs (no dry cycle). While this doesn't compare with your home washer, it's basically 10 days of clothes for two travelers including towels. For a family of 5, you will probably run two cycles a week.
It also depends on where you want to travel. We traveled across Europe in another vehicle and finding public laundry places was difficult or expensive. Let alone meaning we would have to drive into the center of a city. Was a total pain. The USA has a ton of laundromats, and then they disappear in central and South America, replaced by laundry services of varying quality. What we didn't like was having to find laundry services every week or so. With a family of 5, it's only going to be more pressing.
The machine when on wash only mode is very efficient and easily run off the batteries <500 watts, for the dry mode (we have a condenser dryer model) it pulls about 1000 watts. So you need beefy batteries or shore power to dry. If it's hot and nice outside we run a wash only cycle and hang it up. Wash uses about 10 gallons of water. So you do need some tankage (we carry about 100 gallons).
Overall if you have the space, get one. These little items of comfort make the journey a lot less taxing, which equates to a happier life. Now, I would never put a washer/dryer in our Vanagon Syncro because the space it uses, but if you have a bigger rig, we found the trade-off worth it.