5) \( 5 \sqrt{20} \times 3 \sqrt{15} \)

To simplify \( 5 \sqrt{20} \times 3 \sqrt{15} \), first break down the square roots: \(\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}\), so \(5 \sqrt{20} = 5(2\sqrt{5}) = 10\sqrt{5}\). Next, for \(3 \sqrt{15}\), it stays the same as it cannot be simplified further. Now, multiply: \[ 10\sqrt{5} \times 3\sqrt{15} = 30\sqrt{5 \times 15} = 30\sqrt{75} = 30\sqrt{25 \times 3} = 30 \times 5\sqrt{3} = 150\sqrt{3}. \] So, the final answer is \( 150\sqrt{3} \). Have fun visualizing that you’re multiplying ingredients in a magical potion! Imagine how much fun it would be to tell someone you have 150 of those mysterious "sqrt" creatures! For math lovers, understanding square roots can open doors to higher concepts such as imaginary numbers. Delve into how these numbers work in complex equations; they might just change your perspective on math forever.