1. **State the problem:** Factor the quadratic expression $x^2 + 6x + 5$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multiply to $ac$ and add to $b$. 3. **Apply to our problem:** 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 factored form:** Using these numbers, the factorization is $$(x + 1)(x + 5).$$ 6. **Verify by expansion:** Expanding $(x + 1)(x + 5)$ gives $x^2 + 5x + 1x + 5 = x^2 + 6x + 5$, confirming the factorization is correct. **Final answer:** $$(x + 1)(x + 5)$$