Answer
$$\cos \theta= \frac{-33}{65}$$
Work Step by Step
Let u=(3,4),\quad v=(5,-12), $\quad =u\cdot v $.
The angle $\theta$ between $u$ and $v$ is given by the formula
$$\cos \theta=\frac{}{\|u\| \cdot\|v\|}=\frac{15-48}{\sqrt{ 25+144}\sqrt{ 9+16}}=\frac{-33}{5 \times 13}=\frac{-33}{65}.$$
