$$ \begin{aligned} \frac{7-2x}{x+3} &= 5&& \text{multiply ALL terms by } \color{blue}{ x+3 }. \\[1 em](x+3)\frac{7-2x}{x+3} &= (x+3)\cdot5&& \text{cancel out the denominators} \\[1 em]7-2x &= 5x+15&& \text{move the $ \color{blue}{ 5x } $ to the left side and $ \color{blue}{ 7 }$ to the right} \\[1 em]-2x-5x &= 15-7&& \text{simplify left and right hand side} \\[1 em]-7x &= 8&& \text{ divide both sides by $ -7 $ } \\[1 em]x &= -\frac{8}{7}&& \\[1 em] \end{aligned} $$

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