$5x+13$ là bội của $2x+1$
$⇒ 5x+13 ⋮ 2x+1$
$⇒ 2(5x+13) ⋮ 2x+1$
$= 10x+26 ⋮ 2x+1$
$= (10x+5)+21 ⋮ 2x+1$
$= 5(2x+1)+21 ⋮ 2x+1$
vì $5(2x+1) ⋮ 2x+1$
$⇒ 21 ⋮ 2x+1$
$⇒ 2x+1∈Ư(21)=${$±1;±3;±7;±21$}
$⇒ 2x∈${$0;±2;-4;6;-8;-22;20$}
$⇒ x∈${$0;±1;-2;3;4;-11;10$}
vì $x$ nguyên dương
$⇒ x∈${$1;3;4;10$}