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\mathrm{ \lim _{x \rightarrow \infty} \ln \left(\frac{x+5}{x}\right)^x \text { equals }}

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\lim _{x \rightarrow \infty} \ln \left(\left(\frac{x+5}{x}\right)^x\right)=\lim _{x \rightarrow \infty} \ln \left(\left(1+\frac{5}{x}\right)^x\right)=\lim _{x \rightarrow \infty} x \cdot \ln \left(1+\frac{5}{x}\right)=5

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