Simplify (-5 square root of -6)( square root of 5)

$(- 5 \sqrt{- 6}) (\sqrt{5})$

Rewrite $- 6$ as $- 1 (6)$ .

$- 5 \sqrt{- 1 (6)} \sqrt{5}$

Rewrite $\sqrt{- 1 (6)}$ as $\sqrt{- 1} \cdot \sqrt{6}$ .

$- 5 (\sqrt{- 1} \cdot \sqrt{6}) \sqrt{5}$

Rewrite $\sqrt{- 1}$ as $i$ .

$- 5 (i \cdot \sqrt{6}) \sqrt{5}$

Multiply $- 5 i \sqrt{6} \sqrt{5}$ .

Combine using the product rule for radicals.

$- 5 i \sqrt{5 \cdot 6}$

Multiply $5$ by $6$ .

$- 5 i \sqrt{30}$