Add the fifths, then the sevenths. \[ \begin{aligned} & \frac{4}{5}+\frac{2}{7}+1 \frac{1}{5}+\frac{5}{7} \\ = & \left(\frac{4}{5}+1 \frac{1}{5}\right)+\left(\frac{2}{7}+\frac{5}{7}\right) \\ = & \square+\square\end{aligned} \]

To add the fifths, we begin with \(\frac{4}{5}\) and \(1 \frac{1}{5}\). Convert \(1 \frac{1}{5}\) into an improper fraction: \[ 1 \frac{1}{5} = 1 + \frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5}. \] Now, we can add \(\frac{4}{5}\) and \(\frac{6}{5}\): \[ \frac{4}{5} + \frac{6}{5} = \frac{4 + 6}{5} = \frac{10}{5} = 2. \] Next, we add the sevenths, \(\frac{2}{7}\) and \(\frac{5}{7}\): \[ \frac{2}{7} + \frac{5}{7} = \frac{2 + 5}{7} = \frac{7}{7} = 1. \] Putting it all together: \[ \left(\frac{4}{5} + 1 \frac{1}{5}\right) + \left(\frac{2}{7} + \frac{5}{7}\right) = 2 + 1. \] So, filling in the boxes: \[ \boxed{2}+\boxed{1}. \]