This might help ...
Lagrange's theorem: For any finite group $G,$ the order (number of elements) of every subgroup $L$ of $G$ divides the order of $G.$
$G$ has $15$ elements.
Factors of $15$ are $1,3,5,$ and $15.$
Since, the given size of $L$ is at least $4$ $(1$ and $3$ eliminated$)$ and not equal to $G(15$ eliminated$),$ the only size left is $5.$
Size of $L$ is $5.$