jmc

The sum of the angle measures in a polygon with $n$ sides is $180(n-2)$ degrees. So, the sum of the pentagon's angles is $180(5-2)=540$ degrees.

Let $\angle C$ and $\angle D$ each have measure $x$, so $\angle E=2x+15^{\circ }$. Therefore, we must have $$60^{\circ }+85^{\circ }+x+x+2x+15^{\circ }=540^{\circ }.$$ Simplifying the left side gives $4x+160^{\circ }=540^{\circ }$, so $4x=380^{\circ }$ and $x=95^{\circ }$. This means the largest angle has measure $2x+15^{\circ }=190^{\circ }+15^{\circ }=\boxed{205^{\circ }}$.