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