$$ \begin{aligned} \frac{x-1}{5} &= \frac{x+5}{15}&& \text{multiply ALL terms by } \color{blue}{ 15 }. \\[1 em]15 \cdot \frac{x-1}{5} &= 15 \cdot \frac{x+5}{15}&& \text{cancel out the denominators} \\[1 em]3x-3 &= x+5&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ -3 }$ to the right} \\[1 em]3x-x &= 5+3&& \text{simplify left and right hand side} \\[1 em]2x &= 8&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= \frac{8}{2}&& \\[1 em]x &= 4&& \\[1 em] \end{aligned} $$

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