evaluate \sqrt{13^2-5^2}

To evaluate the expression, we first simplify the expression under the square root:

$\sqrt{13^2-5^2} = \sqrt{169-25} = \sqrt{144}$

Since $144$ is a perfect square, we can take the square root:

$\sqrt{144} = 12$

Therefore, $\sqrt{13^2-5^2} = \boxed{12}$.