Incorrect: May 30th, 1975
Correct: May 30, 1975
When you’re writing out a date like May 30, 1975 (in the American style), the day is written as a cardinal number. So you should never write May 30th, 1975. The weird thing though is when you’re speaking. Even though it is written as May 30, you say, “May thirtieth” (30th). So when you are reading a date that is written May 30, 1975, you say “May thirtieth, nineteen seventy-five.” That’s probably why a lot of people get confused about how to write it.
The instance in which it is OK to use an ordinal number is when you are writing the 30th of May, because you are placing the day in a series:, meaning of all the days in May, this day is the thirtieth.