$$ \begin{aligned} 5x\cdot5-\frac{5}{5}+1 &= 0&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]55x\cdot5-5\cdot\frac{5}{5}+5\cdot1 &= 5\cdot0&& \text{cancel out the denominators} \\[1 em]125x-5+5 &= 0&& \text{simplify left side} \\[1 em]125x-5+5 &= 0&& \\[1 em]125x &= 0&& \text{ divide both sides by $ 125 $ } \\[1 em]x &= \frac{0}{125}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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