1992 AIME Problem 15

Define a positive integer n^{}_{} to be a factorial tail if there is some positive integer m^{}_{} such that the decimal representation of m! ends with exactly n zeroes. How many positive integers less than 1992 are not factorial tails?

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.