1. The problem asks for the coordinate notation representing a translation left 5 units followed by a 180 degree rotation around the origin. 2. Translation left 5 units means subtracting 5 from the x-coordinate: $ (x, y) \to (x - 5, y) $. 3. A 180 degree rotation around the origin transforms any point $ (x, y) $ to $ (-x, -y) $. 4. We apply the translation first, then the rotation: Start with $ (x, y) $. After translation left 5 units: $ (x - 5, y) $. After 180 degree rotation: $ (-(x - 5), -y) = (-x + 5, -y) $. 5. Therefore, the coordinate notation is $ (x, y) \to (-x + 5, -y) $. 6. Checking the options, the correct one is $ (x, y) \to (-x + 5, -y) $.