Correct spelling, explanation: the word 25th is an abbreviation of twenty-fifth. As you can see, it’s one of the regularly inflected ordinal numbers. That’s why it has to be spelled with -th suffix. You can’t change its ending, because this numeral doesn’t end with number one. 25th is the correct version and 25st is incorrect.

Definition of 25th:
numeral, a number that comes between twenty-fourth and twenty-sixth
I wonder what the 25th century would be like.
December 25th is the day I want to spend with my family.

Incorrect spelling, explanation: 25st is a misspelling because we cannot use the ending -st for ordinal numbers that don’t end with number one (which inflects as first), because the abbreviation wouldn’t match with the expansion. The full form of 25th is twenty-fifth. It’s important to remember that only the first three numbers (and numerals ending with one of them) in English have different, irregular suffixes. That’s the reason this ordinal number is spelled 25th, not 25st.

Incorrect spelling

Incorrect spelling