\[5\sqrt{2} - 4\sqrt{8} + 3\sqrt{32} =\]
\[= 5\sqrt{2} - 4\sqrt{2 \cdot 4} + 3\sqrt{2 \cdot 16} =\]
\[= 5\sqrt{2} - 8\sqrt{2} + 12\sqrt{2} = 9\sqrt{2}\]