\begin{gather*} P(\text{5th as second}) = P(\text{LL...LAA}) \\ = 4 \cdot \frac{13 \cdot 12 \cdot \cdot 11 \cdot 2 \cdot 1}{15 \cdot 14 \cdot 13 \cdot 12 \cdot 11} = \frac{8}{15 \cdot 14}. \end{gather*}