Answer
$\log _{4}\dfrac {\left( x-1\right) }{\left( x+1\right) ^{4}}$
Work Step by Step
We use the rules of logarithms to obtain:
$\log _{4}\left( x^{2}-1\right) -5\log _{4}\left( x+1\right) =\log _{4}\left( x^{2}-1\right) -\log _{4}\left( x+1\right) ^{5}=\log _{4}\dfrac {x^{2}-1}{\left( x+1\right) ^5}=\log _{4}\dfrac {\left( x+1\right) \left( x-1\right) }{\left( x+1\right) ^{5}}=\log _{4}\dfrac {\left( x-1\right) }{\left( x+1\right) ^{4}}$
