Hello Dermita and welcome to the RTA forums !

The way things are at the moment I would say you have a reasonable chance of crossing the Sierras on the Tioga Pass in late May. I think the snow pack is around 70% of average this year, but there is just no way of knowing for sure as a few late snow storms can change things quite dramatically.

I hope you have allowed time enough for your journey to enjoy Yosemite Valley, as it is also beautiful and the waterfalls should be flowing nicely, and other areas of the park like Glacier point and Mariposa Grove.