By the definition of big-Oh, we need to find a real constant $c > 0$ and an integer constant $n_0 \geq 1$ such that $(n+1)^5 \leq c(n^5)$ for every integer $n \geq n_0$. Since $(n+1)^5=n^5+5n^4+10n^3+10n^2+5n+1$, $(n+1)^5 \leq c(n^5)$ for $c = 8$ and $n\geq n_0 = 2$.