Differentiate. \[ f(x)=\ln \left(\frac{x^{3}-5}{x}\right) \] \[ f^{\prime}(x)= \]

Step 1 ：Given the function \(f(x)=\ln \left(\frac{x^{3}-5}{x}\right)\), we are asked to find its derivative.

Step 2 ：First, we can simplify the function by splitting the natural logarithm into two parts using the properties of logarithms: \(f(x) = -\ln(x) + \ln(x^{3} - 5)\).

Step 3 ：Next, we differentiate each part separately using the chain rule and the quotient rule.

Step 4 ：The derivative of \(-\ln(x)\) is \(-\frac{1}{x}\) and the derivative of \(\ln(x^{3} - 5)\) is \(\frac{3x^{2}}{x^{3}-5}\).

Step 5 ：Adding these two derivatives together, we find the derivative of the original function: \(f^{\prime}(x)=\frac{3x^{2}}{x^{3}-5}-\frac{1}{x}\).

Step 6 ：Final Answer: \(f^{\prime}(x)=\boxed{\frac{3x^{2}}{x^{3}-5}-\frac{1}{x}}\)