1. The problem is to simplify the expression $5x^2 + 5x$. 2. We use the distributive property which states that $a(b + c) = ab + ac$. 3. Factor out the common factor $5x$ from both terms: $$5x^2 + 5x = 5x(x + 1)$$ 4. This is the simplified form of the expression. So, the final answer is: $$5x(x + 1)$$