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We are given two functions:
\[
f(x) = 5 - 5x \quad \text{and} \quad g(x) = -3x^2 + 5
\]
We need to find \((f + g)(x)\), which is the sum of \(f(x)\) and \(g(x)\).

To solve this:
\[
(f + g)(x) = f(x) + g(x)
\]
Substitute the given functions:
\[
(f + g)(x) = (5 - 5x) + (-3x^2 + 5)
\]
Now, combine like terms:
\[
(f + g)(x) = -3x^2 - 5x + (5 + 5) = -3x^2 - 5x + 10
\]

Thus, the correct answer is:
\[
\boxed{-3x^2 - 5x + 10}
\]

This corresponds to option **A**.

Would you like a more detailed explanation? Here are five related questions to explore this further:

1. What is the general process of combining two functions?
2. How do you identify and combine like terms in polynomial expressions?
3. What happens if one or both functions are more complex (e.g., contain higher-degree terms)?
4. How would you graph the function \(f(x) + g(x)\)?
5. Can this method be extended to more than two functions?

**Tip**: Always align similar terms (e.g., \(x^2\), \(x\), and constants) to avoid errors when combining functions.

If f(x) = 5 - 5x and g(x) = -3x^2 + 5, find (f + g)(x).

Learn how to add the functions f(x) = 5 - 5x and g(x) = -3x^2 + 5. This problem involves key algebraic concepts such as polynomial addition and combining like terms. Suitable for students in Grades 8-10.

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