Answer
$60$
Work Step by Step
The number of arrangements of choosing $r$ objects out of $n$ distinct objects $(r \leq n)$ is:
$(a)$ If order matters, use permutation, i.e, $P(n,r)$.
$(b)$ If order doesn't matter, use combination, i.e, $C(n,r)$.
Here, order matters since different order means different codes.
Therefore, $P(5,3) = 5 \times 4 \times 3 = 60$
