In how many ways can $5$ balls be placed in $4$ tins if any number of balls can be placed in any tin?

$5$ balls can be placed in any of the $4$ tins.

Therefore, we can say that each balls can be paced in any of the $4$ tins.

Therefore, number of ways of arranging balls in all $4$ tins $=4\times 4\times 4\times 4\times 4=4^5$