What you mean by "... I would like my formula to find all the dates ..."
Do you want the formula to return "Yes" or "No" for every row of table depending the date in some column of same row? When yes, then probably something like (assuming the dates are in column A of table, and they aren't datestrings, but are real dates)
Code:
=AND(DAY(A2)<=15,MONTH(A2) = 5)