$7 \frac{2}{3}+2 \frac{1}{5}$

Step 1 ：Convert the mixed numbers into improper fractions: \(7 \frac{2}{3} = \frac{23}{3}\) and \(2 \frac{1}{5} = \frac{11}{5}\)

Step 2 ：Find a common denominator and add the fractions: \(\frac{23}{3} + \frac{11}{5} = \frac{23 \times 5 + 11 \times 3}{3 \times 5} = \frac{148}{15}\)

Step 3 ：\(\boxed{9 \frac{13}{15}}\)