AMC 10 2020a Problem 3

Assuming $a\neq3$ , $b\neq4$ , and $c\neq5$ , what is the value in simplest form of the following expression? $$\frac{a-3}{5-c} \cdot \frac{b-4}{3-a} \cdot \frac{c-5}{4-b}$$ $\textbf{(A) } -1 \textbf{(B) } 1 \textbf{(C) } \frac{abc}{60} \textbf{(D) } \frac{1}{abc} - \frac{1}{60} \textbf{(E) } \frac{1}{60} - \frac{1}{abc}$