Most definitely.... do not pass up Grand Teton Nat'l Park. Your 5th wheel would fit in either Colter Bay or Gros Ventre (our favorite) campgrounds in the park. Both are dry camping and neither takes reservations but they each have 300 sites and we've never had a problem getting a site.
Since you're in West Yellowstone, plan on leaving early morning before the crowds start forming and drive through the park and out the southern exit into Grand Teton. Liklihood of seeing more critters when leaving early and also you want to get to the Teton campgrounds as early as you can.
Each park is completely different in looks and things to do. Grand Teton has the best trails of all abilities. Enjoy! Also scour their web sites for lots of good information on things to do, road information, camping information and special 'alerts'.
https://www.nps.gov/grte/index.htmhttps://www.nps.gov/yell/planyourvisit/index.htm