It varies year to year, and impossible to predict in advanced. The problem with May is usually not snow at that point, although there's still plenty covering some the trails at higher altitudes, and fresh dustings are not impossible. It's that the weather can be very cloudy and rainy. Those mountain views aren't doing much good behind a veil of clouds. Some of the trails can be very muddy due to the snow run-off and accumulated rain.
Late in the month of May is probably worth the gamble IF you budget enough time. Give yourself at least two, ideally three full days, and be prepared to lose at least one day to weather.
PS- And I often repeat this: checking the average temperature for the month is not very useful for transitional times like spring or fall, because the mathematical mean conceals a much larger range of temperatures than in summer or winter. You would need the average plus the standard deviation to make any kind of reasonable assumption.