Let \(y = \frac{3}{2x+5}\).

Rearrange to make \(x\) the subject: \(2x + 5 = \frac{3}{y}\).

Multiply both sides by \(y\): \(y(2x + 5) = 3\).

Expand: \(2xy + 5y = 3\).

Rearrange to isolate \(x\): \(2xy = 3 - 5y\).

Divide by \(2y\): \(x = \frac{3 - 5y}{2y}\).

Thus, \(f^{-1}(x) = \frac{3 - 5x}{2x}\).