Let's assume the number of cars manufactured per day in country B is x.
According to the given information, the number of cars manufactured per day in country A is 5 times the number in country B, which is 5x.
The total number of cars manufactured per day in both countries is 39,606.
So, we can set up the equation: x + 5x = 39,606.
Simplifying the equation, we get 6x = 39,606.
Dividing both sides of the equation by 6, we find that x = 6,601.
Therefore, the number of cars manufactured per day in country B is 6,601, and the number in country A is 5 times that, which is 33,005.