Assuming you mean mixed fractions, we have
[tex]5\dfrac{1}{6}=5+\dfrac{1}{6}[/tex]
and
[tex]3\dfrac{5}{6}=3+\dfrac{5}{6}[/tex]
So,
[tex]5\dfrac{1}{6}-3\dfrac{5}{6}=5+\dfrac{1}{6}-3-\dfrac{5}{6}=2-\dfrac{4}{6}=2-\dfrac{2}{3}[/tex]
If you want to write this as a fraction, you have
[tex]2-\dfrac{2}{3} = \dfrac{6}{3}-\dfrac{2}{3}=\dfrac{4}{3}[/tex]
If you want to write this as a mixed fraction, you have
[tex]2-\dfrac{2}{3}=1+\dfrac{3}{3}-\dfrac{2}{3}=1+\dfrac{1}{3}=1\dfrac{1}{3}[/tex]
