$$ \begin{aligned} \frac{x+2}{4} &= \frac{x+5}{5}&& \text{multiply ALL terms by } \color{blue}{ 20 }. \\[1 em]20 \cdot \frac{x+2}{4} &= 20 \cdot \frac{x+5}{5}&& \text{cancel out the denominators} \\[1 em]5x+10 &= 4x+20&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ 10 }$ to the right} \\[1 em]5x-4x &= 20-10&& \text{simplify left and right hand side} \\[1 em]x &= 10&& \\[1 em]x &= 10&& \\[1 em] \end{aligned} $$

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