$$ \begin{aligned} \frac{1}{4}p+\frac{5}{8}p &= 5&& \text{multiply ALL terms by } \color{blue}{ 8 }. \\[1 em]8 \cdot \frac{1}{4}p+8\frac{5}{8}p &= 8\cdot5&& \text{cancel out the denominators} \\[1 em]2p+5p &= 40&& \text{simplify left side} \\[1 em]7p &= 40&& \text{ divide both sides by $ 7 $ } \\[1 em]p &= \frac{40}{7}&& \\[1 em] \end{aligned} $$

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