Find the inverse function of $f$ informally. \[ \begin{array}{l} f(x)=5 x+9 \\ f^{-1}(x)= \end{array} \]

Step 1 ：\(y = 5x + 9\)

Step 2 ：\(x = 5y + 9\)

Step 3 ：\(x - 9 = 5y\)

Step 4 ：\(y = \frac{x - 9}{5}\)

Step 5 ：\(f^{-1}(x) = \frac{x - 9}{5}\)

Step 6 ：\(f^{-1}(f(x)) = \frac{5x + 9 - 9}{5} = x\)

Step 7 ：\(\boxed{f^{-1}(x) = \frac{x - 9}{5}}\)