The earth is a spherical object which has a translational (orbital) velocity equal to 67,000 mph and a rotational velocity of 1,040 mph. do you think there is magnus force acting on the earth?

No, there is no magnus force on the earth.

Magnus force is the force on any spinning object from the air by creating a pressure difference as the air drags with the spin.

Earth is a very huge mass with gravitational force that holds air around it. The air also spin due to gravitational effect but there is no pressure difference created by spinning earth. So, gravitational force is the only force that governs the motion of earth. And beyond small atmosphere there is empty space or vacuum so there is no magnus force at all.

There is coriolis force seen on air due to rotation of earth not drag force.

with 5 seconds, no, but over time if the police car stays at 65m/s ad the speeding car stays at 60, then obviously yes, but the answer to your question would be, no.

hope this : )