  For a finite group $G$, we consider the problem of counting simultaneous
conjugacy classes of $n$-tuples and simultaneous conjugacy classes of commuting
$n$-tuples in $G$. Let $\alpha_{G,n}$ denote the number of simultaneous
conjugacy classes of $n$-tuples, and $\beta_{G,n}$ the number of simultaneous
conjugacy classes of commuting $n$-tuples in $G$. The generating functions
$A_G(t) = \sum_{n\geq 0} \alpha_{G,n}t^n,$ and $B_G(t) = \sum_{n\geq 0}
\beta_{G,n}t^n$ are rational functions of $t$. This paper concern studied of
normalized functions $A_G(t/|G|)$ and $B_G(t/|G|)$ for finite $p$-groups of
rank at most $5$.
