#### Answer

$-5x+\frac{5}{6}y-1$

#### Work Step by Step

We are given the expression $\frac{1}{2}(10x-2)-\frac{1}{6}(60x-5y)$. We can use the distributive property and then group like terms to simplify.
$\frac{1}{2}\times(10x-2)-\frac{1}{6}\times(60x-5y)=5x-1-10x+\frac{5}{6}y$
=$(5x+(-10x))+\frac{5}{6}y-1=-5x+\frac{5}{6}y-1$