1. **State the problem:** We are given the function $$f(x) = \frac{1}{2} \cdot 4^x + 3$$ and asked to find the value of its inverse function $$f^{-1}$$ at $$x = 5$$. 2. **Recall the definition of inverse function:** The inverse function $$f^{-1}(y)$$ gives the value of $$x$$ such that $$f(x) = y$$. 3. **Set up the equation:** To find $$f^{-1}(5)$$, solve for $$x$$ in the equation: $$ 5 = \frac{1}{2} \cdot 4^x + 3 $$ 4. **Isolate the exponential term:** $$ 5 - 3 = \frac{1}{2} \cdot 4^x $$ $$ 2 = \frac{1}{2} \cdot 4^x $$ 5. **Multiply both sides by 2 to clear the fraction:** $$ 2 \times 2 = \cancel{2} \times \frac{1}{\cancel{2}} \cdot 4^x $$ $$ 4 = 4^x $$ 6. **Rewrite 4 as a power of 4:** $$ 4 = 4^1 $$ 7. **Since bases are equal, set exponents equal:** $$ x = 1 $$ 8. **Conclusion:** $$f^{-1}(5) = 1$$ **Answer:** Option C. 1