To find the roots of the quadratic equation \(x^2 + 5x + 6 = 0\), we can use factoring.

1. Factor the quadratic equation:

We need to find two numbers that multiply to 6 (the constant term) and add up to 5 (the coefficient of \(x\)).

These numbers are 2 and 3, because:
\[
2 \times 3 = 6
\]
\[
2 + 3 = 5
\]

2. Write the quadratic equation in factored form:

\[
x^2 + 5x + 6 = (x + 2)(x + 3)
\]

3. Set each factor equal to zero to find the roots:

\[
x + 2 = 0 \quad \text{or} \quad x + 3 = 0
\]
\[
x = -2 \quad \text{or} \quad x = -3
\]

So, the roots of the equation are:

C. -2, -3