Beartooth pass is awesome and I'd suggest putting it high on the list but May might be too early.
It is indeed high, about 11,000 feet above sea level!:) A beautiful drive. I have a sister who is afraid of heights and she was more or less hyperventilating while driving over it but wouldn't let me take the wheel. I'll never go over it again with her driving:)
We drove Bear Tooth Pass on May 15 and for 11 miles, it was solid snow and ice. I sure was wishing I was in my pickup with the studded snow tires.
I am from the South, sure didn't expect to see that kind of snow in May.