If \( n \in N \) and \( \Delta_{n}=\left|\begin{array}{ccc}n ! & (n+1) ! & (n+2) ! \\ (n+1) ! & ...

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If \( n \in N \) and \( \Delta_{n}=\left|\begin{array}{ccc}n ! & (n+1) ! & (n+2) ! \\ (n+1) ! & (n+2) ! & (n+3) ! \\ (n+2) ! & (n+3) ! & (n+4) !\end{array}\right| \) then \( \lim _{n \rightarrow \infty} \frac{\left(3 n^{3}-5\right) \Delta_{n}}{\Delta_{n+1}} \) equals
(a) \( \frac{3}{2} \)
(b) \( \frac{5}{2} \)
(c) \( -\frac{5}{2} \)
(d) 3
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