$$ \begin{aligned} \frac{x}{3} &= \frac{4}{5}-\frac{x-5}{8}&& \text{multiply ALL terms by } \color{blue}{ 120 }. \\[1 em]120 \cdot \frac{x}{3} &= 120\cdot\frac{4}{5}-120\frac{x-5}{8}&& \text{cancel out the denominators} \\[1 em]40x &= 96-(15x-75)&& \text{simplify right side} \\[1 em]40x &= 96-15x+75&& \\[1 em]40x &= -15x+171&& \text{move the $ \color{blue}{ -15x } $ to the left side} \\[1 em]40x+15x &= 171&& \text{simplify left side} \\[1 em]55x &= 171&& \text{ divide both sides by $ 55 $ } \\[1 em]x &= \frac{171}{55}&& \\[1 em] \end{aligned} $$

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