Lời giải chi tiết:

\(A_n^2 - 3C_n^2 = 15 - 5n{\rm{ }}\left( * \right)\)

ĐKXĐ:\(n \ge 2,n \in N \)

\(\left( * \right) \Leftrightarrow \frac{{n!}}{{\left( {n - 2} \right)!}} - 3.\frac{{n!}}{{\left( {n - 2} \right)!2!}} = 15 - 5n\)

\( \Leftrightarrow  - \frac{1}{2}n\left( {n - 1} \right) = 15 - 5n\)

\( \Leftrightarrow  - \frac{1}{2}{n^2} + \frac{1}{2}n - 15 + 5n = 0\)

\( \Leftrightarrow  - \frac{1}{2}{n^2} + \frac{{11}}{2}n - 15 = 0\)

\( \Rightarrow \left[ \begin{array}{l}n = 6\\n = 5\end{array} \right.\left( {t/m} \right)\)

Chọn A.