$$ \begin{aligned} 13-2m+\frac{3}{4} &= 5m+10&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4\cdot13-4\cdot2m+4\cdot\frac{3}{4} &= 4\cdot5m+4\cdot10&& \text{cancel out the denominators} \\[1 em]52-8m+3 &= 20m+40&& \text{simplify left side} \\[1 em]-8m+55 &= 20m+40&& \text{move the $ \color{blue}{ 20m } $ to the left side and $ \color{blue}{ 55 }$ to the right} \\[1 em]-8m-20m &= 40-55&& \text{simplify left and right hand side} \\[1 em]-28m &= -15&& \text{ divide both sides by $ -28 $ } \\[1 em]m &= \frac{-15}{-28}&& \\[1 em]m &= \frac{15}{28}&& \\[1 em] \end{aligned} $$

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