\begin{equation*}
\begin{split}
& 5\frac{1}{2} + 3\frac{2}{3} - 1\frac{1}{5}\\\\
& 5 + \frac{1}{2} + 3 + \frac{2}{3} - 1 - \frac{1}{5}\\\\
& (5 + 3 - 1) + \left(\frac{1}{2} + \frac{2}{3} - \frac{1}{5}\right)\\\\
& 7 + \left(\frac{1 \times \color{red} 15 }{2 \times\color{red} 15} + \frac{2 \times \color{red} 10}{3 \times \color{red} 10} - \frac{1 \times \color{red} 6 }{5 \times \color{red} 6 }\right)\\\\
& 7 + \frac{15 + 20 - 6}{30}\\\\
& 7 + \frac{29}{30}\\\\
& 7\frac{29}{30}
\end{split}
\end{equation*}
