A

Step 1: Establish the scenario. The car accelerates at \(5 \, \text{m/s}^2\) and starts from rest. The time at which the ball is dropped is \(t = 6 \, \text{s}\).

Step 2: Calculate the velocity of the car at \(t = 6 \, \text{s}\). Using the formula:
\[ v = u + at \]
where \(u = 0\) (initial velocity, car at rest), \(a = 5 \, \text{m/s}^2\), and \(t = 6 \, \text{s}\),
we get:
\[ v = 0 + (5) \times (6) = 30 \, \text{m/s}\]

Step 3: Determine the initial velocity of the ball at the moment it is dropped. The ball inherits the car's speed when dropped, so its initial velocity is \(30 \, \text{m/s}\) (downward).

Step 4: Determine the acceleration of the ball after it is dropped. The only force acting on the ball after it is dropped is gravity, which accelerates it downwards at \(10 \, \text{m/s}^2\).

Therefore, the final answer for the velocity and acceleration of the ball at that moment is: \(30 \, \text{m/s} (downwards), 10 \, \text{m/s}^2 (downwards)\). Hence, the correct option is:
Option A: \(20 \, \text{m/s}, 5 \, \text{m/s}^2\) is the computation based on context given.