The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have
[tex](-5,\ 7)\to x_1=-5,\ y_1=7\\(4,\ -2)\to x_2=4,\ y_2=-2[/tex]
Substitute:
[tex]d=\sqrt{(4-(-5))^2+(-2-7)^2}=\sqrt{9^2+(-9)^2}=\sqrt{81+81}=\sqrt{81\cdot2}\\\\=\sqrt{81}\cdot\sqrt2=\boxed{9\sqrt2}[/tex]
