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

1. Problem Description

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

2. Solution Steps

First, simplify each square root by finding the largest perfect square factor:

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

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

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

Now substitute the simplified square roots into the expression:

$8\sqrt{5} - 4\sqrt{5} + 5\sqrt{7}$

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

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

3. Final Answer

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