Write the first five terms of the sequences whose nth term is

$a_{n}=\frac{n}{n+1}$

Substituting $n=1,2,3,4,5$, we obtain

$a_{1}=\frac{1}{1+1}=\frac{1}{2}, a_{2}=\frac{2}{2+1}=\frac{2}{3}, a_{3}=\frac{3}{3+1}=\frac{3}{4}, a_{4}=\frac{4}{4+1}=\frac{4}{5}, a_{5}=\frac{5}{5+1}=\frac{5}{6}$

Therefore, the required terms are $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}$, and $\frac{5}{6}$.