How many different numbers of 5-digit can be formed by using the digits 2,3, 4, 5 and 7, without repetition, so that the number is not divisible by 5?

Number of digit available = 5 (all distinct)
Number of digits to be used = 5
                   
Since the number is not divisible by 5.
   5 cannot occupy box 5.
       Number of permutations for box                       ...(i)
       Now, we have 4-digits and 4 boxes.
        Number of permutations =                                 ... (ii)
        From (i) and (ii), the total number of permutations = 4 x 24 = 96
        Hence, the number of numbers formed, that are not divisible by 5 = 96.