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

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