Yeah. Unless it's a very dry snow season (hope not), many of the high roads and passes will still be closed in May.

I've had good luck in May closer to Lake Tahoe. Kingsbury Grade, Mount Rose Highway, Carson Pass, and Luther Pass stay open all winter. Caltrans always tries to open Ebbetts Pass by Memorial Day (but I'm pretty sure they didn't make that date this year). In May, you should still be able to ride up Ebbetts most of the way before hitting unplowed road. Monitor Pass usually opens sooner than Ebbetts. In this very snow year, Monitor opened on May 12.

Lower elevation roads are just about guaranteed to be open in May. In the Bay Area, Mt Hamilton Road is the king, occasionally closed for snow. Do it front and back for an extra challenge. Also, Mt. Diablo is a great climb with amazing views at the top. Mt Tamalpais is number 3 of the Bay Area mountains, but it's always seemed "meh" to me.

Many choices for climbing in Southern California, although I'm not as familiar with that area. A few I've ridden in May or sooner: Gibraltar Rd out of Santa Barbara, Figueroa Mountain out of Solvang (though I hear the road surface is getting rough), Mt. Baldy from Claremont, Palomar Mountain, Mt. Laguna from Pine Valley, Montezuma Rd from Borrego Springs to Ranchita.