Answer
$4$
Work Step by Step
Using $\log_bx^m=m\log_bx$ or the Power Rule of Logarithms, the given expression, $
\log_{5}625
,$ is equivalent to
\begin{array}{l}\require{cancel}
\log_{5}5^4
\\\\=
4\log_{5}5
.\end{array}
Since $\log_bb=1,$ the expression, $
4\log_{5}5
,$ simplifies to
\begin{array}{l}\require{cancel}
4(1)
\\\\=
4
.\end{array}