Helping prove this notation for Big-O(n!)
Remember that $\Theta(5n \log n^5) = \Theta(n \log n)$, since constant factors don't matter.

Then $\Theta(n \log n) = \Omega(n \log n)$, by the definition of big theta.

$\Omega(n \log n) = \Omega(n)$, because log is monotonic increasing (so we can remove it and still have a valid lower bound).

Finally, $\Omega(n) = \Omega(n^{2/3})$, by the properties of power functions.