$\frac{\text{x}-5}{2}-\frac{\text{x}-3}{5}=\frac{1}{2}$
$\Rightarrow10\Big(\frac{\text{x}-5}{2}\Big)-10\Big(\frac{\text{x}-3}{5}\Big)=10\Big(\frac{1}{2}\Big)$
(multiplying throughout by 10, which is the L.C.M. of 2, 2 and 5):
$\Rightarrow5(\text{x}-5)-2(\text{x}-3)=5$
$\Rightarrow5\text{x}-2$
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