jmc

We can simplify: $$\ell (y)=\frac{1}{2y-10}.$$ The fraction $\frac{1}{2y-10}$ fails to be defined only if the denominator is zero. This occurs when $y$ is the solution of the equation $$2y-10=0,$$ which is $y=5$. Thus the domain of $\ell (y)$ is $\boxed{(-\infty ,5)\cup (5,\infty )}$.