1. The problem asks for the derivative of the function $f(x) = 5$. 2. Recall that the derivative of a constant function is always zero because the function does not change as $x$ changes. 3. The formula for the derivative of a constant $c$ is: $$\frac{d}{dx}[c] = 0$$ 4. Since $f(x) = 5$ is a constant function, its derivative is: $$f'(x) = 0$$ 5. Therefore, the correct answer is option d. 0.