$$5 = \frac{5}{3}x+1$$

$$ \begin{aligned} 5 &= \frac{5}{3}x+1&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3\cdot5 &= 3 \cdot \frac{5}{3}x+3\cdot1&& \text{cancel out the denominators} \\[1 em]15 &= 5x+3&& \text{ swap the left and right side of the equation } \\[1 em]5x+3 &= 15&& \text{ move 3 to the right } \\[1 em]5x &= 15-3&& \\[1 em]5x &= 12&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= \frac{12}{5}&& \\[1 em] \end{aligned} $$

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