1. **State the problem:** Simplify the expression $\sqrt{2}(-\sqrt{3} + \sqrt{5})$. 2. **Recall the distributive property:** When multiplying a term by a sum or difference inside parentheses, multiply the term by each part inside the parentheses separately. 3. **Apply the distributive property:** $$\sqrt{2}(-\sqrt{3} + \sqrt{5}) = \sqrt{2} \times (-\sqrt{3}) + \sqrt{2} \times \sqrt{5}$$ 4. **Multiply the terms:** $$= -\sqrt{2} \times \sqrt{3} + \sqrt{2} \times \sqrt{5}$$ 5. **Use the property of square roots:** $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$ 6. **Simplify each term:** $$= -\sqrt{6} + \sqrt{10}$$ 7. **Final answer:** The simplified form of the expression is $$-\sqrt{6} + \sqrt{10}$$ This is the simplest form since $\sqrt{6}$ and $\sqrt{10}$ cannot be simplified further or combined.