To find five rational numbers between $1 \frac{1}{3}$ (which is $\frac{4}{3}$) and $\frac{1}{3}$, we can first express both of these as improper fractions with the same denominator. Then, we can identify rational numbers between them.

1. Convert to improper fractions:

   • $1 \frac{1}{3} = \frac{4}{3}$
   • $\frac{1}{3}$ remains as it is.