Given
[tex]5\frac{2}{5}-6\frac{5}{7}[/tex]To subtract both fractions, the first step is to express the mixed fractions as improper fractions.
[tex]5\frac{2}{5}=\frac{5\cdot5}{5}+\frac{2}{5}=\frac{25}{5}+\frac{2}{5}=\frac{27}{5}[/tex][tex]6\frac{5}{7}=6+\frac{5}{7}=\frac{6\cdot7}{7}+\frac{5}{7}=\frac{42}{7}+\frac{5}{7}=\frac{47}{7}[/tex]The subtraction expressed as improper fractions are
[tex]\frac{27}{5}-\frac{47}{7}[/tex]Second, you have to find the common denominator between 5 and 7 and express both fractions under said the common denominator. The common denominator for 5 and 7 is 35
To express the first fraction with denominator 35 you have to multiply both the numerator and denominator by 7
To express the second fraction with denominator 35, you have to multiply both the numerator and denominator by 5
[tex]\begin{gathered} \frac{27\cdot7}{5\cdot7}-\frac{47\cdot5}{7\cdot5}=\frac{189}{35}-\frac{235}{35} \\ \frac{189-235}{35} \\ \frac{-46}{35} \end{gathered}[/tex]The result of the calculation is
[tex]-\frac{46}{35}[/tex]Expressed as a mixed fraction the result is
[tex]-1\frac{11}{35}[/tex]