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First, let's convert the mixed numbers into improper fractions. For \( 5 \frac{5}{5} \), this is equivalent to \( 5 + 1 = 6 \) since \( \frac{5}{5} = 1 \). So we have \( 6 - 2 \frac{1}{5} \). Now, we convert \( 2 \frac{1}{5} \) to improper form, which gives us \( 2 + \frac{1}{5} = 2 \frac{5}{5} + \frac{1}{5} = \frac{10}{5} + \frac{1}{5} = \frac{11}{5} \). Now, we simplify \( 6 - \frac{11}{5} \). To do this, we’ll convert \( 6 \) to a fraction with a denominator of \( 5 \): \( 6 = \frac{30}{5} \). So now we can subtract: \[ \frac{30}{5} - \frac{11}{5} = \frac{30 - 11}{5} = \frac{19}{5} \] Finally, we can convert \( \frac{19}{5} \) back into a mixed number, which gives us \( 3 \frac{4}{5} \). Thus, \( 5 \frac{5}{5}-2 \frac{1}{5} = 3 \frac{4}{5} \).