Answer
$-\frac{1}{2}$
Work Step by Step
We use the addition formula for cosine, $\cos(s+t)=\cos s\cos t-\sin s\sin t$, with $s=\frac{13\pi}{15}$ and $t=-\frac{\pi}{5}$.
$\cos(\frac{13\pi}{15}) \cos(-\frac{\pi}{5})-\sin(\frac{13\pi}{15})\sin(-\frac{\pi}{5})$
$=\cos(\frac{13\pi}{15}+(-\frac{\pi}{5}))$
$=\cos(\frac{13\pi}{15}-\frac{3\pi}{15})$
$=\cos(\frac{10\pi}{15})$
$=\cos(\frac{2\pi}{3})$
$=-\frac{1}{2}$
