5-Rank of ambiguous class groups of quintic Kummer extensions

Let $k \,=\, \mathbb{Q}(\sqrt[5]{n},\zeta_5)$, where $n$ is a positive integer, $5^{th}$ power-free, whose $5-$class group isomorphic to $\mathbb{Z}/5\mathbb{Z}\times\mathbb{Z}/5\mathbb{Z}$. $k_0\,=\,\mathbb{Q}(\zeta_5)$ be the cyclotomic field containing primitive root of unity $\zeta_5$. $C_{k,5}^{(\sigma)}$ ambiguous classes under action $Gal(k/k_0)$ = $<\sigma>$. The aim this paper determine all integers such that has rank $1$ or $2$.