Removing arithmetic within recurrences
The link doesn't say what you say it does.  I don't see the number 180 appearing anywhere on that link.  And that link doesn't say the purpose is to prove $T(n) \le 5 n \log n$ for all $n \ge 0$; it says to prove that $T(n) = O(n \log n)$.  Check the definition of big-O notation; it doesn't require proving $T(n) \le c n \log n$ for all $n \ge 0$; it suffices to prove it for all $n \ge 180$ (or for all $n \ge n_0$ for any other constant $n_0$ of your choice).