May or early June probably means that Tioga Pass on the west side of the park is still snowed in. Many of the park campgrounds are closed this year meaning that commercial parks will have even more people trying to get in.
Park entryYou should read thru the rest of that park site for more info. And get the partk app on your phone.
Yosemite like Yellowstone and some other major parks is huge, it takes hours to drive places especially if you are camped outside the park. Like many of us Yosemite is our favorite but difficult to get in and far away for us. And worst it is in the evil empire of Cali.
That said my wife won a 7 day pass to a commercial cg on the east so we hope to be there this summer.
I cannot advise you on cg since we always stay inside the park, until this year but you better make reservations ASAP if you hope to find a spot. May could see snow on the ground in the park.