Let the lines \( y + 2x = \sqrt{11} + 7\sqrt{7} \) and \( 2y + x = 2\sqrt{11} + 6\sqrt{7} \) be normal to a circle \( C : (x - h)^2 + (y - k)^2 = r^2 \). If the line \( \sqrt{11}y - 3x = \frac{5\sqrt{77}}{3} + 11 \) is tangent to the circle \( C \), then the value of \( (5h - 8k)^2 + 5r^2 \) is equal to ________.
