(1) In the arithmetic sequence $\left\{a_{n}\right\}$, $a_{1}>0$, and $5 a_{8}=8 a_{13}$. Then the value of $n$ when the sum of the first $n$ terms $S_{n}$ reaches its maximum is ( ).
(A) 20
(B) 21
(C) 22
(D) 23
(1) B Hint: From $5 a_{8}=8 a_{13}$, we get $5\left(a_{1}+7 d\right)=8\left(a_{1}+12 d\right)$, which means $d=$ $-\frac{3}{61} a_{1}$, and by
$$
a_{n}=a_{1}+(n-1) d=a_{1}+(n-1)\left(-\frac{3}{61} a_{1}\right) \geqslant 0,
$$

we get $n \leqslant \frac{64}{3}$, so the first 21 terms of the sequence are positive, and all subsequent terms are negative, hence the sum of the first $n$ terms $S_{n}$ reaches its maximum value when $n$ is 21.