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