The function \(f(x) = 2x + 5\) is a linear function with a positive gradient of 2 and a \(y\)-intercept of 5.

To find the inverse function \(f^{-1}(x)\), we swap \(x\) and \(y\) in the equation \(y = 2x + 5\) and solve for \(y\):

\(x = 2y + 5\)

\(x - 5 = 2y\)

\(y = \frac{x - 5}{2}\)

Thus, \(f^{-1}(x) = \frac{x - 5}{2}\), which is also a linear function with a positive gradient of \(\frac{1}{2}\) and a \(y\)-intercept of \(-\frac{5}{2}\).

The line \(y = x\) is the line of symmetry between \(y = f(x)\) and \(y = f^{-1}(x)\), indicating that the graphs are reflections of each other across this line.