Harmonically Monotonic

Let $a_n = \dfrac 1{a+(n-1)d}$ , where $n \in \mathbb N$ . Then $a_1 = \dfrac 1a = 5$ , $\implies a = \dfrac 15$ . And $a_{20} = \dfrac 1{a+19d} = 25$ , $\implies d = \dfrac {\frac 1{25}-\frac 15}{19} = - \dfrac 4{475}$ . Then,

$\begin{aligned} a_n & < 0 \\ \frac 1{a+(n-1)d} & < 0 \\ a+(n-1) d & < 0 \\ \frac 15 - \frac {4(n-1)}{475} & < 0 \\ n & > \frac {95}4+1 = 24.25 \\ \implies n & > \boxed{25} \end{aligned}$