If $x>5$, then which of the given numbers is the smallest?
(a) $5 / x$
(b) $5 /(x+1)$
(c) $5 /(x-1)$
(d) $x / 5$
(e) $(x+1) / 5$
The correct option is (b).

Since $x>5$, we have $0<x-1<x<x+1$. Therefore, $\frac{5}{x+1}<\frac{5}{x}<\frac{5}{x-1}$. We also have $\frac{5}{x}<1<\frac{x}{5}<\frac{x+1}{5}$, since $5<x<x+1$. Thus, among the numbers $\frac{5}{x}$, $\frac{5}{x+1}$, $\frac{5}{x-1}$, $\frac{x}{5}$, and $\frac{x+1}{5}$, the smallest is $\frac{5}{x+1}$.