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-\frac{24}{40}-\frac{35}{40}
Least common multiple of 5 and 8 is 40. Convert -\frac{3}{5} and \frac{7}{8} to fractions with denominator 40.
\frac{-24-35}{40}
Since -\frac{24}{40} and \frac{35}{40} have the same denominator, subtract them by subtracting their numerators.
-\frac{59}{40}
Subtract 35 from -24 to get -59.