How many $4-digit$ numbers can be formed with the digits $0,2,3,4,5$ when a digit may be repeated any number of times in any arrangement?

First digit can't be $0$, so first digit can be placed up with $4$ ways only
however, the next $3$ places may be filled by any of the numbers 
Required number of numbers $=(4\times 5\times 5\times 5)=500$.