$$\textbf{Step - 1: Define Rational number}$$
$$\text{A rational number, in Mathematics, can be defined as any number which can be represented}$$
$$\text{ in the form of } \dfrac{{p}}{{q}} \text{ ,where } q \neq 0 $$
$$\textbf{Step - 2: Change the question into rational number}$$
$$\text{The rational numbers of } 1 \text{ and } 2, \text{ is } \dfrac{{10}}{{10}} \text{ and } \dfrac{{20}}{{10}}.$$
$$\text{Rational numbers between } \dfrac{{10}}{{10}} \text{ and } \dfrac{{20}}{{10}} \text{ are } \dfrac{{11}}{{10}}, \dfrac{{12}}{{10}}, \dfrac{{13}}{{10}}, \dfrac{{14}}{{10}}, \dfrac{{15}}{{10}}, \dfrac{{16}}{{10}}, \dfrac{{17}}{{10}}, \dfrac{{18}}{{10}} \text{ and } \dfrac{{19}}{{10}}$$
$$\textbf{Hence, five rational numbers between 1} \textbf{ and 2} \textbf{ are } \mathbf{\dfrac{{11}}{{10}}, \dfrac{{12}}{{10}}, \dfrac{{13}}{{10}}, \dfrac{{14}}{{10}}}\textbf{ and }\mathbf{\dfrac{{15}}{{10}}}$$