1. **State the problem:** We need to find the sum of the two polynomials $5x^2 + 3x - 7$ and $12x + 12$. 2. **Formula used:** To add polynomials, add the coefficients of like terms (terms with the same power of $x$). 3. **Identify like terms:** - $5x^2$ has no like term in the second polynomial. - $3x$ and $12x$ are like terms. - $-7$ and $12$ are constant terms. 4. **Add the like terms:** $$ 5x^2 + (3x + 12x) + (-7 + 12) = 5x^2 + 15x + 5 $$ 5. **Final answer:** The sum is $5x^2 + 15x + 5$, which corresponds to option A.