Wow, May is a tough time for sure... Most the good rams are pushing the snowline heading up and away...
If it was November, I'd have many spots for you to go!
You may be able to catch the Sullivan lake rams before they climb too high in NE Washington...
Actually, a spot I just remembered is in Central Washington near Ellensburg and Yakima...you can get on those rams all year round..easy country, easy access.
Let me know if you are interested. Desert/foothills type country.
Ernie