2005 AMC 10B Problem 4

Each inner expression evaluates to $$5 \diamond 12 = \sqrt{5^2 + 12^2} = 13$$ and similarly $(-12) \diamond (-5)$ $= \sqrt{144 + 25} = 13.$ Then $$13 \diamond 13 = \sqrt{13^2 + 13^2} = 13\sqrt{2}.$$ Thus, D is the correct answer.