jmc

We use the distance formula: $\sqrt{(2-(-3){)}^2+((-5)-7{)}^2}=\sqrt{25+144}=\boxed{13}$.

- OR -

We note that the points $(-3,7)$, $(2,-5)$, and $(-3,-5)$ form a right triangle with legs of length 5 and 12. This is a Pythagorean triple, so the hypotenuse has length $\boxed{13}$.