$$ \begin{aligned} 5x\cdot5-5+\frac{5}{5} &= 0&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]55x\cdot5-5\cdot5+5\cdot\frac{5}{5} &= 5\cdot0&& \text{cancel out the denominators} \\[1 em]125x-25+5 &= 0&& \text{simplify left side} \\[1 em]125x-20 &= 0&& \text{ move the constants to the right } \\[1 em]125x &= 20&& \text{ divide both sides by $ 125 $ } \\[1 em]x &= \frac{20}{125}&& \\[1 em]x &= \frac{4}{25}&& \\[1 em] \end{aligned} $$

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