Let \( f: S \rightarrow S \) where \( S=(0, \infty) \) be a twice P...

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Let \( f: S \rightarrow S \) where \( S=(0, \infty) \) be a twice
P differentiable function such that \( f(x+1)=x f(x) \). If
\( \mathrm{W} \) \( g: S \rightarrow R \) be defined as \( g(x)=\log _{e} f(x) \), then the value of \( \left|g^{\prime \prime}(5)-g^{\prime \prime}(1)\right| \) is equal to:
(A) \( \frac{205}{144} \)
(B) \( \frac{197}{144} \)
(C) \( \frac{187}{144} \)
(D) 1
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