What day is the May 5th Fog?

There is no such thing as five fogs in the 24 solar terms.

The twenty-four solar terms are:

Beginning of spring, rain, sting, vernal equinox, Qingming, Grain Rain.

Long summer, small full, boundless, summer solstice, small Shu, big Shu.

Beginning of autumn, Chushu, Bailu, Autumnal Equinox, Cold Dew, First Frost.

Beginning of winter, light snow, heavy snow, winter solstice, slight cold, severe cold.

The origin of solar terms:

During the period of Emperor Wu of the Western Han Dynasty, "Twenty-four solar terms" were included in taichu calendar as a supplement to guide the agricultural calendar. The day with the longest sun shadow and the shortest day (the shortest day) is determined as the winter solstice in the Yellow River basin by the method of soil returning to the sun shadow measurement (the average time method).

Taking the winter solstice as the starting point of the "twenty-four solar terms", the winter solstice and the next winter solstice are divided into 24 equal parts, the time between each solar term is equal, and the interval between each solar term is 15 days. The solar terms divided by the "Land Returning to the Sun Shadow Law" list the winter solstice as the first of the "twenty-four solar terms", starting from the winter solstice and ending with heavy snow.