The problem asks us to combine and simplify the expression $5\sqrt{54} + \sqrt{24}$.

1. Problem Description

The problem asks us to combine and simplify the expression $5\sqrt{54} + \sqrt{24}$.

2. Solution Steps

First, we simplify the radicals.

$\sqrt{54} = \sqrt{9 \cdot 6} = \sqrt{9} \cdot \sqrt{6} = 3\sqrt{6}$.

$\sqrt{24} = \sqrt{4 \cdot 6} = \sqrt{4} \cdot \sqrt{6} = 2\sqrt{6}$.

Therefore,

$5\sqrt{54} + \sqrt{24} = 5(3\sqrt{6}) + 2\sqrt{6} = 15\sqrt{6} + 2\sqrt{6} = (15+2)\sqrt{6} = 17\sqrt{6}$.

3. Final Answer

$17\sqrt{6}$