Visiting in May
Yosemite's waterfalls (mostly in Yosemite Valley) usually peak in mid- to late-May, so this is the best month to see them. While it may seem like summer, snow is usually present in much of the park, and the Tioga and Glacier Point Roads may be closed.
The Tioga Road (Highway 120 through the park) and Glacier Point Road are closed, typically until late May or early June. While it's impossible to predict when these roads will open because April and May weather significantly affect plowing, you view a list of opening dates since 1980 to get a feel for when they can open.
Areas to Visit
The road to the Mariposa Grove of Giant Sequoias is usually open, although parking is limited. It's best park at the Wawona Store and use the free shuttle from there to the Mariposa Grove. (Exact operating dates of the shuttle vary depending on conditions.)
Hetch Hetchy, a valley similar to Yosemite Valley that was dammed, is generally snow-free and Wapama and Tueeulala Falls are full.
Hiking and Backpacking
Outside of Yosemite Valley, trails in Wawona, Mariposa Grove, and Hetch Hetchy are usually snow-free, but may be wet.
Few multi-night backpacking options are available in May, depending on conditions. The trails in best condition will be those leaving from Yosemite Valley, Wawona, and Hetch Hetchy, but it's unlikely you'll be able to find a hike more than two nights long that doesn't involve significant snow. Wilderness permits are required and may be difficult to get.
The Upper, Lower, and North Pines (Yosemite Valley), Wawona, and Hodgdon Meadow Campgrounds are on the reservation system with no sites available the same day.
Horse/mule rides: The Valley Stable typically opens in late April, conditions permitting.
Biking: Bicycle paths in Yosemite Valley are snow-free in May and an excellent way to get around eastern Yosemite Valley. Bikes are available for rent at Yosemite Lodge and Curry Village.
Rafting: The Merced River is usually closed to rafting and kayaking in May, except following relatively dry winters.