$$ \begin{aligned} \frac{x}{x+5} &= \frac{2}{3}&& \text{multiply ALL terms by } \color{blue}{ (x+5)\cdot3 }. \\[1 em](x+5)\cdot3 \cdot \frac{x}{x+5} &= (x+5)\cdot3\cdot\frac{2}{3}&& \text{cancel out the denominators} \\[1 em]3x &= 2x+10&& \text{move the $ \color{blue}{ 2x } $ to the left side} \\[1 em]3x-2x &= 10&& \text{simplify left side} \\[1 em]x &= 10&& \\[1 em]x &= 10&& \\[1 em] \end{aligned} $$

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