1. The problem is to add the mixed numbers $2 \ 1/5$ and $3 \ 2/5$.\n2. Convert each mixed number to an improper fraction.\n For $2 \ 1/5$: integer part is 2, denominator is 5, numerator is 1.\n Calculate numerator: $2 \times 5 + 1 = 10 + 1 = 11$.\n So, $2 \ 1/5 = \dfrac{11}{5}$.\n3. For $3 \ 2/5$: integer part is 3, denominator is 5, numerator is 2.\n Calculate numerator: $3 \times 5 + 2 = 15 + 2 = 17$.\n So, $3 \ 2/5 = \dfrac{17}{5}$.\n4. Now add the two improper fractions: $\dfrac{11}{5} + \dfrac{17}{5} = \dfrac{11 + 17}{5} = \dfrac{28}{5}$.\n5. The result is $\dfrac{28}{5}$, which is an improper fraction.\nFinal answer: $\dfrac{28}{5}$