5. $$6\sqrt{2} - (\sqrt{8} - (\sqrt{50} - \sqrt{162}))$$

Преобразуем выражение:

$$\sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2}$$

$$\sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2}$$

$$\sqrt{162} = \sqrt{81 \cdot 2} = 9\sqrt{2}$$

Тогда:

$$6\sqrt{2} - (2\sqrt{2} - (5\sqrt{2} - 9\sqrt{2})) = 6\sqrt{2} - (2\sqrt{2} - (-4\sqrt{2})) = 6\sqrt{2} - (2\sqrt{2} + 4\sqrt{2}) = 6\sqrt{2} - 6\sqrt{2} = 0$$

Ответ: 0