Answer
An explicit rule for the sequence is
$a_n=5(-5)^{n-1}$
Work Step by Step
The given recursive rule is
$a_1=5,a_n=-5a_{n-1}$
First term is $a_1=5$.
and common ratio $r=-5$.
Explicit rule for an geometric sequence.
$\Rightarrow a_n=a_1r^{n-1}$
Substitute $5$ for $a_1$ and $-5$ for $r$.
$\Rightarrow a_n=5(-5)^{n-1}$