jmc

We use the distance formula: $\sqrt{(-4-1{)}^2+(1-13{)}^2},$ which is $\sqrt{25+144}=\sqrt{169}=\boxed{13}$.

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We note that the points $(-4,1)$, $(1,13)$, and $(1,1)$ form a right triangle with legs of length 5 and 12. $(5,12,13)$ is a Pythagorean triple, so the hypotenuse has length $\boxed{13}$.