Answer
$\sqrt {113}-5$
Work Step by Step
Step 1. Rewrite the equation as $(x-8)^2+(y-7)^2=25$
Step 2. The center of the circle can be found at $(8,7)$ and the point giving the shortest distance should be on the line connecting this center to the origin.
Step 3. The distance from the origin to the center of the circle is $d=\sqrt {8^2+7^2}=\sqrt {113}$
Step 4. The shortest distance can be found as $d_m=d-r=\sqrt {113}-5$
