$$\frac{4x+5}{2} = x-\frac{1}{5}$$

$$ \begin{aligned} \frac{4x+5}{2} &= x-\frac{1}{5}&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10 \cdot \frac{4x+5}{2} &= 10x-10\cdot\frac{1}{5}&& \text{cancel out the denominators} \\[1 em]20x+25 &= 10x-2&& \text{move the $ \color{blue}{ 10x } $ to the left side and $ \color{blue}{ 25 }$ to the right} \\[1 em]20x-10x &= -2-25&& \text{simplify left and right hand side} \\[1 em]10x &= -27&& \text{ divide both sides by $ 10 $ } \\[1 em]x &= -\frac{27}{10}&& \\[1 em] \end{aligned} $$

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