1. **State the problem:** Solve the equation $ (x+3)^2 - (x^2 + 6x) = 5 $ for $x$. 2. **Recall formulas and rules:** - Square of a binomial: $ (a+b)^2 = a^2 + 2ab + b^2 $. - Simplify expressions by expanding and combining like terms. 3. **Expand the left side:** $$ (x+3)^2 = x^2 + 2 \cdot x \cdot 3 + 3^2 = x^2 + 6x + 9 $$ 4. **Substitute back into the equation:** $$ x^2 + 6x + 9 - (x^2 + 6x) = 5 $$ 5. **Distribute the minus sign:** $$ x^2 + 6x + 9 - x^2 - 6x = 5 $$ 6. **Combine like terms:** $$ \cancel{x^2} + \cancel{6x} + 9 - \cancel{x^2} - \cancel{6x} = 5 $$ $$ 9 = 5 $$ 7. **Analyze the result:** The equation simplifies to $9 = 5$, which is false. 8. **Conclusion:** Since the simplified equation is a contradiction, there is **no solution** to the original equation. **Final answer:** No solution.