Represent $\dfrac{13}{5} \text{ and } \dfrac{-13}{5}$ on the number line.

Draw a number line and mark a point O on it, representing the integer 0. Mark the integers to the right (1, 2, 3) and to the left (-1, -2, -3).

Convert each of the given improper fractions into a mixed fraction to find the two integers between which it lies.

$\Rightarrow \dfrac{13}{5} = 2\dfrac{3}{5} \\[1em] \Rightarrow \dfrac{-13}{5} = -2\dfrac{3}{5}$

So, $\dfrac{13}{5}$ lies between 2 and 3, and $\dfrac{-13}{5}$ lies between -2 and -3.

Divide the unit length between 2 and 3, as well as the unit length between -2 and -3, into 5 equal segments by making 4 equally spaced marks in each interval.

For $\dfrac{13}{5}$ : Starting from the integer 2, count forward (to the right) 3 segments. Label this specific position as point A, representing $2\dfrac{3}{5}$ i.e. $\dfrac{13}{5}$.

For $\dfrac{-13}{5}$ : Starting from the integer -2, count backward (to the left) 3 segments. Label this specific position as point B, representing $-2\dfrac{3}{5}$ i.e. $\dfrac{-13}{5}$, as shown below :

Hence, the points A and B on the number line represent $\mathbf{\dfrac{13}{5} \text{ and } \dfrac{-13}{5}}$.