1. **Stating the problem:** Factor the quadratic expression $x^2 + 6x + 5$. 2. **Formula and rules:** To factor a quadratic expression of the form $ax^2 + bx + c$, we look for two numbers that multiply to $ac$ and add to $b$. 3. **Identify values:** Here, $a=1$, $b=6$, and $c=5$. We need two numbers that multiply to $1 \times 5 = 5$ and add to $6$. 4. **Find the numbers:** The numbers are $1$ and $5$ because $1 \times 5 = 5$ and $1 + 5 = 6$. 5. **Write the factors:** Using these numbers, the factorization is $(x + 1)(x + 5)$. 6. **Check by expansion:** Expanding $(x + 1)(x + 5)$ gives $x^2 + 5x + 1x + 5 = x^2 + 6x + 5$, which matches the original expression. 7. **Final answer:** The factored form is $(x + 1)(x + 5)$.