1. **State the problem:** Simplify the expression $\left(3\sqrt{0.4} + \sqrt{10}\right) \sqrt{2.5}$.\n\n2. **Recall the properties of square roots:** $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$. This allows us to multiply square roots inside the expression.\n\n3. **Rewrite the expression:** $\left(3\sqrt{0.4} + \sqrt{10}\right) \sqrt{2.5} = 3\sqrt{0.4} \times \sqrt{2.5} + \sqrt{10} \times \sqrt{2.5}$.\n\n4. **Multiply inside the square roots:** $3\sqrt{0.4 \times 2.5} + \sqrt{10 \times 2.5}$.\n\n5. **Calculate the products inside the roots:** $0.4 \times 2.5 = 1$ and $10 \times 2.5 = 25$. So the expression becomes $3\sqrt{1} + \sqrt{25}$.\n\n6. **Simplify the square roots:** $\sqrt{1} = 1$ and $\sqrt{25} = 5$. So the expression is $3 \times 1 + 5 = 3 + 5$.\n\n7. **Add the terms:** $3 + 5 = 8$.\n\n**Final answer:** $8$