1. The problem is to simplify the expression $5\sqrt{2} + 5\sqrt{2}$.\n\n2. We use the property of like terms in algebra: terms with the same radical part can be added by adding their coefficients.\n\n3. Here, both terms have the radical part $\sqrt{2}$. So, we add the coefficients: $5 + 5 = 10$.\n\n4. Therefore, $5\sqrt{2} + 5\sqrt{2} = 10\sqrt{2}$.\n\n5. The simplified form of the expression is $10\sqrt{2}$.