Answer
$a_{n}=\displaystyle \frac{n^{3}}{5^{n+1}}, \quad n=1,2,3...$
Work Step by Step
Observe numerators and denominators separately, as sequences. Annotate $a_{n}=\displaystyle \frac{A_{n}}{B_{n}}$
The numerators are cubes of natural numbers,
$1^{3},2^{3},3^{3},4^{3}...\qquad A_{n}=n^{3}$
The denominators are powers of 5,
$25=5^{2}\qquad(5^{n+1}$ when n=$1)$
$125=5^{3}\qquad(5^{n+1}$ when n=$2$
$625=5^{4}\qquad(5^{n+1}$ when n=$3)$
$3125=5^{5}\qquad(5^{n+1}$ when n=$4)$
etc.
Thus, $B_{n}=5^{n+1},$ and
$a_{n}=\displaystyle \frac{n^{3}}{5^{n+1}}, \quad n=1,2,3...$
