The nth term of an AP is $a_n=(5n-2)/3$. Find its common difference.

$a_1=(5-2)/3=1$ and $a_2=(10-2)/3=8/3$, so $d=8/3-1=5/3$. In general $a_n=(5/3)n-2/3$, and the coefficient of $n$ is the common difference. Answering 5 reads the coefficient before dividing by 3; 1 is the first term, not $d$; -2/3 is the constant part.