1. **State the problem:** Given the function $f(x) = \frac{1}{4} \cdot 2^x$ and $x = 5$, find $f(5)$. 2. **Formula used:** The function is an exponential function defined as $f(x) = \frac{1}{4} \cdot 2^x$. To find the value at $x=5$, substitute 5 into the function. 3. **Substitute and calculate:** $$f(5) = \frac{1}{4} \cdot 2^5$$ Calculate $2^5$: $$2^5 = 32$$ So, $$f(5) = \frac{1}{4} \cdot 32$$ 4. **Simplify the multiplication:** $$f(5) = \frac{1}{4} \cdot 32 = \frac{32}{4}$$ 5. **Simplify the fraction:** $$f(5) = \cancel{\frac{32}{4}} = 8$$ 6. **Final answer:** $$\boxed{8}$$ This means when $x=5$, the function value $f(5)$ is 8.