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\frac{10}{5\left(-5\right)}
Divide \frac{1}{5} by \frac{-5}{10} by multiplying \frac{1}{5} by the reciprocal of \frac{-5}{10}.
\frac{10}{-25}
Multiply 5 and -5 to get -25.
-\frac{2}{5}
Reduce the fraction \frac{10}{-25} to lowest terms by extracting and canceling out 5.