The problem is to simplify the expression $\sqrt{320} - \sqrt{80} + \frac{\sqrt{175}}{\sqrt{9}}$.

1. Problem Description

The problem is to simplify the expression $\sqrt{320} - \sqrt{80} + \frac{\sqrt{175}}{\sqrt{9}}$.

2. Solution Steps

First, simplify each of the square roots.

$\sqrt{320} = \sqrt{64 \cdot 5} = \sqrt{64} \cdot \sqrt{5} = 8\sqrt{5}$.

$\sqrt{80} = \sqrt{16 \cdot 5} = \sqrt{16} \cdot \sqrt{5} = 4\sqrt{5}$.

$\sqrt{175} = \sqrt{25 \cdot 7} = \sqrt{25} \cdot \sqrt{7} = 5\sqrt{7}$.

$\sqrt{9} = 3$.

Now, substitute the simplified expressions into the original expression:

$8\sqrt{5} - 4\sqrt{5} + \frac{5\sqrt{7}}{3}$.

Combine the terms with $\sqrt{5}$:

$(8-4)\sqrt{5} + \frac{5\sqrt{7}}{3} = 4\sqrt{5} + \frac{5\sqrt{7}}{3}$.

3. Final Answer

$4\sqrt{5} + \frac{5\sqrt{7}}{3}$