Answer
$-2$
Work Step by Step
Using $\log_bx^m=m\log_bx$ or the Power Rule of Logarithms, the given expression, $
\log_{5}\dfrac{1}{25}
,$ is
\begin{array}{l}\require{cancel}
\log_{5}25^{-1}
\\\\=
\log_{5}(5^2)^{-1}
\\\\=
\log_{5}5^{-2}
\\\\=
-2\log_{5}5
.\end{array}
Since the $\log_bb=1,$ the expression, $
-2\log_{5}5
,$ simplifies to
\begin{array}{l}\require{cancel}
-2(1)
\\\\=
-2
.\end{array}