Simplify cube root of 64- square root of -16-5 square root of -9

$\sqrt[3]{64} - \sqrt{- 16} - 5 \sqrt{- 9}$

Simplify each term.

Rewrite $64$ as $4^{3}$ .

$\sqrt[3]{4^{3}} - \sqrt{- 16} - 5 \sqrt{- 9}$

Pull terms out from under the radical, assuming real numbers.

$4 - \sqrt{- 16} - 5 \sqrt{- 9}$

Rewrite $- 16$ as $- 1 (16)$ .

$4 - \sqrt{- 1 (16)} - 5 \sqrt{- 9}$

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$4 - (\sqrt{- 1} \cdot \sqrt{16}) - 5 \sqrt{- 9}$

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

$4 - (i \cdot \sqrt{16}) - 5 \sqrt{- 9}$

Rewrite $16$ as $4^{2}$ .

$4 - (i \cdot \sqrt{4^{2}}) - 5 \sqrt{- 9}$

Pull terms out from under the radical, assuming positive real numbers.

$4 - (i \cdot 4) - 5 \sqrt{- 9}$

Move $4$ to the left of $i$ .

$4 - (4 \cdot i) - 5 \sqrt{- 9}$

Multiply $4$ by $- 1$ .

$4 - 4 i - 5 \sqrt{- 9}$

Rewrite $- 9$ as $- 1 (9)$ .

$4 - 4 i - 5 \sqrt{- 1 (9)}$

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$4 - 4 i - 5 (\sqrt{- 1} \cdot \sqrt{9})$

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

$4 - 4 i - 5 (i \cdot \sqrt{9})$

Rewrite $9$ as $3^{2}$ .

$4 - 4 i - 5 (i \cdot \sqrt{3^{2}})$

Pull terms out from under the radical, assuming positive real numbers.

$4 - 4 i - 5 (i \cdot 3)$

Move $3$ to the left of $i$ .

$4 - 4 i - 5 (3 \cdot i)$

Multiply $3$ by $- 5$ .

$4 - 4 i - 15 i$

Subtract $15 i$ from $- 4 i$ .

$4 - 19 i$