Functions question bank (Maths)

For the function $f:[1,\infty) \rightarrow [1,\infty)$ defined by $f(x)=(x-1)^4+1$, among the two statements:
(I) The set $S=\{x \in [1,\infty): f(x)=f^{-1}(x)\}$ contains exactly two elements, and
(II) The set $S=\{x \in [1,\infty): f(x)=f^{-1}(x+1)\}$ is an empty set,

If the domain of the function $f(x) = \sqrt{\log_{(0.6)}\left(\left|\dfrac{2x-5}{x^2-4}\right|\right)}$ is $(-\infty, a] \cup \{b\} \cup [c, d) \cup (e, \infty)$, then the value of $a + b + c + d + e$ is _______.