$\begin{array}{cccccc}\text{Degree}n& 1& 2& 3& 4& 5\\ {\left({\displaystyle {\sum }_{p=3}^{n+2}{p}^n}\right)}^{\frac{1}{n}}& 3& 5& 6& 6.89336& 7.80557\end{array}$