jmc

Let $r$ be the radius of the earth in feet. The girl's feet travel along a circle of radius $r$, while the girl's head travels along a circle of radius $r+5$. The circumference of the first circle is $2\pi r$, while the circumference of the second circle is $2\pi (r+5)=2\pi r+10\pi$. So her head travels $(2\pi r+10\pi )-2\pi r=\boxed{10\pi }$ feet more than her feet.