Use [tex]\lim_{x \to 0}\frac{ \ln{( 1+x )}}{x}=1 [/tex]
[tex] \lim_{x \to 0}\frac{\ln(x+5) - \ln5}{x}
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\\ \lim_{x \to 0}\frac{ \ln{ \frac{x+5}{5} }}{x}
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\\ \lim_{x \to 0}\frac{ \ln{( 1+\frac{x}{5} )}}{x}
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\\ \lim_{x \to 0}\frac{ \ln{( 1+\frac{x}{5} )}}{\frac{x}{5}\times 5}
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\\ \frac{1}{5} \lim_{x \to 0}\frac{ \ln{( 1+\frac{x}{5} )}}{\frac{x}{5}}
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\\ \frac{1}{5} \times 1
\\
\\\frac{1}{5}[/tex]
