Let \( f: S \rightarrow S \) where \( S=(0, \infty) \) be a twice differentiable function such that \( f(x+1)=x f(x) \).…

Let \( f: S \rightarrow S \) where \( S=(0, \infty) \) be a twice differentiable function such that \( f(x+1)=x f(x) \). If \( g: S \rightarrow R \) 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