jmc

We use the distance formula: $$\begin{array}{rl}\sqrt{(2-(-6){)}^2+(y-5{)}^2}& =\sqrt{8^2+(y-5{)}^2}\\ & =\sqrt{y^2-10y+89}\\ & =10.\end{array}$$Squaring both sides and rearranging terms, we find that $$\begin{array}{rl}{y}^2-10y+89& =100\\ y^2-10y-11& =0\\ (y-11)(y+1)& =0\end{array}$$Thus, $y=11$ or $y=-1$. We are given that $y>0$, so $y=\boxed{11}$.