AUSTRIAN-POLISH 1996 Problem 1

Let $k \ge 1$ be a positive integer. Prove that there exist exactly $3^{k-1}$ natural numbers $n$ with the following properties: (i) $n$ has exactly $k$ digits (in decimal representation), (ii) all the digits of $n$ are odd, (iii) $n$ is divisible by $5$ , (iv) the number $m = n/5$ has $k$ odd digits