The number of 3 digit numbers using $1,2,3,4,5$ if no digit is to be used more than once in each number is 

The digits are $1,2,3,4,5$

The number of 3 digit numbers using the digits $1,2,3,4,5$ with out repetition is equal to number of ways of filling three blanks with five digits without repetition. 

The first blank can be filled with any one of five digits in five ways. second blank can be filled the remaining four digits in four ways, third blank can be filled in 3 ways. 

Therefore, the number of 3 digit numbers is $5·4·3=\boxed{60}$