Answer
$-\frac{24}{25}$
Work Step by Step
1. Let $sin^{-1}\frac{3}{5}=u$ (quadrant I), we have $sin(u)=\frac{3}{5}, cos(u)=\frac{4}{5}$
2. Let $cos^{-1}(-\frac{4}{5})=v$ (quadrant II), we have $cos(v)=-\frac{4}{5}, sin(v)=\frac{3}{5}$
3. $sin(u-v)=sin(u)cos(v)-cos(u)sin(v)=(\frac{3}{5})(-\frac{4}{5})-(\frac{4}{5})(\frac{3}{5})=-\frac{24}{25}$