imc

$$\begin{array}{rl}(5\diamond 12)\diamond ((-12)\diamond (-5))& =(\sqrt{5^2+12^2})\diamond (\sqrt{(-12{)}^2+(-5{)}^2})\\ & =(\sqrt{169})\diamond (\sqrt{169})\\ & =13\diamond 13\\ & =\sqrt{13^2+13^2}\\ & =\sqrt{338}\\ & =\boxed{13\sqrt{2}}\end{array}$$ Note that the negative signs did not matter and any number squared times two is that number times the square root of 2.