Would someone please break this down in a simple way on how to solve it.

Since you're finding the sum (adding) all you have to do is combine like terms.
5x ² is by itself because there is no other term with x²
3x and 12x because they have an x
-7 and 12 because they're normal coefficients
Then you're left with 5x² + 15x + 5, answer choice A
Answer:
5x² + 3x - 7 + 12x + 12 = 5x² + 15x + 5
So here we have 3x and 12x, you can see that they have the common factor which is x, so you keep x and add 3 and 12 and we have 15x. For the numbers just calculate as usual. What you have 5x² left, there is no number to subtract or add with it so it will remain unchanged.