Answer
$-15$
Work Step by Step
The dot product of two vectors $\mathbf a$ and $\mathbf b$ is $|\mathbf a||\mathbf b|\cos \theta $, where $\theta $ is the angle between the two vectors.
So if $|\mathbf a|=6$, $|\mathbf b|=5$, and the angle between $\mathbf a$ and $\mathbf b$ is $\frac{2\pi}{3}$, then
$$\mathbf a \cdot \mathbf b=|\mathbf a||\mathbf b|\cos (\frac{2\pi}{3})=6(5)(-\frac{1}{2})=-3(5)=-15.$$
