Answer
$\dfrac {2}{\left( 1+2x\right) \times \ln 5}$
Work Step by Step
$\dfrac {d}{dx}\left( \log _{5}\left( 1+2x\right) \right) =\dfrac {1}{1+2x}\times \dfrac {1}{\ln 5}\times \left( \dfrac {d}{dx}\left( 1+2x\right) \right) =\dfrac {2}{\left( 1+2x\right) \times \ln 5}$
