How do you rationalize the sqrt5/sqrt8?

You can multiply and divide by $\sqrt{8}$ to get:
$\frac{\sqrt{5}}{\sqrt{8}} \cdot \frac{\sqrt{8}}{\sqrt{8}} = \frac{\sqrt{5 \cdot 8}}{8} = \frac{\sqrt{40}}{8} = \frac{\sqrt{4 \cdot 10}}{8} = 2 \frac{\sqrt{10}}{8} = \frac{\sqrt{10}}{4}$