Để :$n+5$ chia hết cho $2n-1$
$⇔2(n+5)$ chia hết cho$2n-1$
$⇔2(n-1)+12$ chia hết cho $2n-1$
$⇔12$ chia hết cho $2n-1$
$⇔2n-1∈Ư(12)$
$⇔2n-1 ∈ {1,-1,2,-2,3,-3,4,-4,6,-6,12,-12}$
$⇔ 2n ∈ {2,0,3,-1,4,-2,5,-3,7,-5,13,-11}$
Mà :$2n$ là số chẵn
$⇒ 2n∈ {2,0,4,-2} $
$⇔n∈{1,0,2,-1}
Chúc bạn học tốt !