Find five rational numbers between $\frac{2}{7}$ and $\frac{2}{5}$.

To find five rational numbers between $\frac{2}{7}$ and $\frac{2}{5}$,we first make the denominators the same by finding the least common multiple $(LCM)$ of $7$ and $5$,which is $35$.
$\frac{2}{7} = \frac{2 \times 5}{7 \times 5} = \frac{10}{35}$
$\frac{2}{5} = \frac{2 \times 7}{5 \times 7} = \frac{14}{35}$
Since we need five rational numbers,we can multiply the numerator and denominator of both fractions by $6$ (or any number greater than $5$):
$\frac{10 \times 6}{35 \times 6} = \frac{60}{210}$
$\frac{14 \times 6}{35 \times 6} = \frac{84}{210}$
Now,we can choose any five rational numbers between $\frac{60}{210}$ and $\frac{84}{210}$,such as $\frac{61}{210}, \frac{62}{210}, \frac{63}{210}, \frac{64}{210}, \text{ and } \frac{65}{210}$.