jmc

The slope of $y=2x+5$ is 2, which means the slope of any line perpendicular to it is $-\frac{1}{2}$. Using the point-slope equation for a line we can find the equation of the second line to be $y-5=-\frac{1}{2}(x-5)$. To find the intersection of this with the first line, we plug $y=2x+5$ into the second equation to get $2x+5-5=-\frac{1}{2}(x-5)\Rightarrow \frac{5}{2}x=\frac{5}{2}\Rightarrow x=1$. Therefore $y=2\cdot 1+5=7$ making the intersection at $\boxed{(1,7)}$.