The other option is to find all the five rational numbers in one step. Since we want five numbers, we write 1 and 2 as rational numbers with denominator 5 + 1, i.e., 1 = $\dfrac{6}{6}$ and 2 = $\dfrac{12}{6}$. Then you can check that $\dfrac{7}{6}$,$\dfrac{8}{6}$,$\dfrac{9}{6}$,$\dfrac{10}{6}$ and $\dfrac{11}{6}$ are all rational numbers between 1 and 2. So, the five numbers are $\dfrac{7}{6}$,$\dfrac{8}{6}$,$\dfrac{9}{6}$,$\dfrac{10}{6}$ and $\dfrac{11}{6}$.