Start with the equation \(\ln(x+5) = 5 + \ln x\).

Subtract \(\ln x\) from both sides to get \(\ln(x+5) - \ln x = 5\).

Use the logarithmic identity \(\ln a - \ln b = \ln \left( \frac{a}{b} \right)\) to rewrite the equation as \(\ln \left( \frac{x+5}{x} \right) = 5\).

Exponentiate both sides to remove the logarithm: \(\frac{x+5}{x} = e^5\).

Multiply both sides by \(x\) to get \(x+5 = xe^5\).

Rearrange to solve for \(x\): \(x - xe^5 = -5\).

Factor out \(x\): \(x(1 - e^5) = -5\).

Solve for \(x\): \(x = \frac{-5}{1 - e^5}\).

Calculate the value: \(x \approx 0.034\).