ĐK: \(\left\{ \begin{array}{l}n - 1 \ge 4\\n - 1 \ge 3\\n - 2 \ge 2\end{array} \right. \Leftrightarrow n \ge 5,n \in N\)

\(\begin{array}{l}C_{n - 1}^4 - C_{n - 1}^3 - \dfrac{5}{4}A_{n - 2}^2 < 0\\ \Leftrightarrow \dfrac{{\left( {n - 1} \right)!}}{{4!\left( {n - 5} \right)!}} - \dfrac{{\left( {n - 1} \right)!}}{{3!\left( {n - 4} \right)!}} - \dfrac{5}{4}\dfrac{{\left( {n - 2} \right)!}}{{\left( {n - 4} \right)!}} < 0\\ \Leftrightarrow \dfrac{{\left( {n - 2} \right)!}}{{\left( {n - 5} \right)!}}\left( {\dfrac{{n - 1}}{{4!}} - \dfrac{{n - 1}}{{3!\left( {n - 4} \right)}} - \dfrac{5}{{4\left( {n - 4} \right)}}} \right) < 0\\ \Leftrightarrow \dfrac{{n - 1}}{{24}} - \dfrac{{n - 1}}{{6\left( {n - 4} \right)}} - \dfrac{5}{{4\left( {n - 4} \right)}} < 0\\ \Leftrightarrow \dfrac{{\left( {n - 1} \right)\left( {n - 4} \right) - 4\left( {n - 1} \right) - 30}}{{24\left( {n - 4} \right)}} < 0\end{array}\)

Vì \(n \ge 5 \Rightarrow n - 4 > 0\) nên

\(bpt \Leftrightarrow \left\{ \begin{array}{l}\left( {n - 1} \right)\left( {n - 4} \right) - 4\left( {n - 1} \right) - 30 < 0\\n \ge 5\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}{n^2} - 9n - 22 < 0\\n \ge 5\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} - 2 < n < 11\\n \ge 5\end{array} \right. \Leftrightarrow 5 \le n < 11\)

Vì \(n \in N \Rightarrow n \in \left\{ {5;6;7;8;9;10} \right\}\)

Vậy có 6 giá trị của n thỏa mãn yêu cầu bài toán.