1. We are asked to factor the quadratic expression x^2 + 6x + 5. 2. The general form of a quadratic is ax^2 + bx + c. To factor, we look for two numbers that multiply to c = 5 and add to b = 6. 3. The pairs of factors of 5 are (1, 5) and (-1, -5). Since 1 + 5 = 6, these are the numbers we need. 4. Rewrite the middle term using 1 and 5: x^2 + 1x + 5x + 5. 5. Group terms to factor by grouping: (x^2 + 1x) + (5x + 5). 6. Factor out the common factors in each group: x(x + 1) + 5(x + 1). 7. Now factor out the common binomial factor: (x + 1)(x + 5). 8. Therefore, the factored form of x^2 + 6x + 5 is (x + 1)(x + 5).