Answer
$$-\frac{\sqrt{3}}{3}$$
Work Step by Step
To evaluate trigonometric functions without a calculator, it is necessary to use the unit circle. Doing this, we find that the function evaluates to:
$$\frac{1}{\tan \left(\frac{5\pi }{3}\right)} \\ \frac{1}{-\sqrt{3}}\\ -\frac{\sqrt{3}}{3}$$