Answer
$$-\sqrt{2}$$
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:
$$\frac{1}{\sin \left(\frac{5\pi }{4}\right)} \\ \frac{1}{-\frac{\sqrt{2}}{2}} \\ -\sqrt{2}$$