The apex of a cone is $S$. The cosine of the angle between generatrices $S A$ and $S B$ is $\frac { 7 } { 8 }$. The angle between $S A$ and the base of the cone is $45 ^ { \circ }$. The area of $\triangle S A B$ is $5 \sqrt { 15 }$. Then the lateral surface area of the cone is $\_\_\_\_$.