The problem is to simplify the expression $5\sqrt{48} - \sqrt{3}$.

1. Problem Description

The problem is to simplify the expression $5\sqrt{48} - \sqrt{3}$.

2. Solution Steps

First, simplify the radical $\sqrt{48}$.

We can write 48 as $16 \times 3$.

Thus, $\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}$.

Now substitute this back into the original expression:

$5\sqrt{48} - \sqrt{3} = 5(4\sqrt{3}) - \sqrt{3} = 20\sqrt{3} - \sqrt{3}$.

Finally, combine the terms:

$20\sqrt{3} - \sqrt{3} = (20 - 1)\sqrt{3} = 19\sqrt{3}$.

3. Final Answer

$19\sqrt{3}$