Step 1 :The function given is an exponential function, where the base of the exponential function is 4, which is greater than 1, and the coefficient of the exponential function is -5, which is less than 0.
Step 2 :As x approaches negative infinity, the value of \(4^x\) approaches 0, and the function \(f(x)\) approaches -9.
Step 3 :As x approaches positive infinity, the value of \(4^x\) approaches positive infinity, but because of the negative coefficient, the function \(f(x)\) approaches negative infinity.
Step 4 :Final Answer: \(\boxed{\text{As } x \rightarrow -\infty, f(x) \rightarrow -9. \text{ As } x \rightarrow \infty, f(x) \rightarrow -\infty.}\)