To find $(f + g)(x)$, we add the functions $f(x)$ and $g(x)$:

$(f + g)(x) = f(x) + g(x)$

Given:

$f(x) = 5x \quad \text{and} \quad g(x) = -x^2 + 4$

Substitute these expressions into $(f + g)(x)$:

$(f + g)(x) = 5x + (-x^2 + 4)$

Simplify:

$(f + g)(x) = -x^2 + 5x + 4$

Thus, the answer is:

$(f + g)(x) = -x^2 + 5x + 4$

This is a polynomial in its simplest form.

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Do you want further explanation or have any questions?
Here are 5 related questions to consider:

1. What is $(f - g)(x)$ for the given $f(x)$ and $g(x)$?
2. How do you find $(f \cdot g)(x)$ for these functions?
3. Can you graph $(f + g)(x)$ and describe its key features?
4. What is the domain of $(f + g)(x)$?
5. How does the degree of a polynomial affect its shape?

Tip: When combining functions, always simplify the expression to ensure it's in its simplest form for easier analysis.