A factorial problem

Number Theory Level 2

$d_n$ is the last nonzero digit of the decimal representation of $n!$ .

Is $d_n$ eventually periodic?

Clarification: $d_n$ is called "eventually periodic" if there exist $k$ and $n_0$ such that $d_{n+k}=d_n$ for all $n\geq n_0.$

Excel in math and science