Answer
$\frac{15!}{5!}=6\times 7\times 8........\times 15=10,897,286,400$
Work Step by Step
Consider the Taylor series
$sinx=x-\frac{1}{3!}x^3+\frac{1}{5!}x^5-.....$
Thus,
$sinx^3=x^3-\frac{1}{3!}x^9+\frac{1}{5!}x^15-.....$
$f^{15}(0)=(sin(x^{3})^{15}(0)=\frac{1}{5!}15!$
Hence,
$\frac{15!}{5!}=6\times 7\times 8........\times 15=10,897,286,400$
