  In this article, we investigate properties of cyclic codes over a finite
non-chain ring
$\mathbb{F}_q+v\mathbb{F}_q+v^2\mathbb{F}_q+v^3\mathbb{F}_q+v^4\mathbb{F}_q,$
where $q=p^r,$ $r$ is a positive integer, $p$ is an odd prime, $4 \mid (p-1),$
and $v^5=v.$ As an application, we construct several quantum error correcting
codes over the finite field $\mathbb{F}_q.$
