Use properties of logarithms to expand the logarithmic expression as much as possible \[ \ln \left(\frac{e^{5}}{13}\right) \]

Step 1 ：Define the variables: \(x\)

Step 2 ：Define the expression: \(\ln \left(\frac{e^{5}}{13}\right)\)

Step 3 ：Expand the expression using properties of logarithms: \(\ln(e^5) - \ln(13)\)

Step 4 ：Simplify the expanded expression using the property \(\ln(e^x) = x\): \(5 - \ln(13)\)

Step 5 ：Final Answer: \(\boxed{5 - \ln(13)}\)