$$ \begin{aligned} \frac{a}{5} &= a-\frac{2}{3}&& \text{multiply ALL terms by } \color{blue}{ 15 }. \\[1 em]15 \cdot \frac{a}{5} &= 15a-15\cdot\frac{2}{3}&& \text{cancel out the denominators} \\[1 em]3a &= 15a-10&& \text{move the $ \color{blue}{ 15a } $ to the left side} \\[1 em]3a-15a &= -10&& \text{simplify left side} \\[1 em]-12a &= -10&& \text{ divide both sides by $ -12 $ } \\[1 em]a &= \frac{-10}{-12}&& \\[1 em]a &= \frac{5}{6}&& \\[1 em] \end{aligned} $$

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