I recently got a CX-5 less than a month ago, and I noticed that when starting the car cold and shifting to D gear, there's a noticeable "jerking" sensation as the car moves forward. After driving for a while and the car warms up, when switching between N and D gear, the jerking sensation is still there but much less noticeable. Is this normal?

My guess is that it might be because the RPM hasn't reached the normal idle speed after starting, plus the effect of the torque converter. I've tried this on other cars, and there are similar situations. After starting, switch to Neutral, release the handbrake and brake, then press the brake again to shift to Drive or Reverse, and this issue doesn't occur.

Try the solution I used before with my Mazda3. Before starting, press the brake pedal, then shift to D gear and wait for about 1-2 seconds. Then release the brake and press the accelerator to move forward. This way, you won't feel a sudden lurch forward.

Shift to N gear first, apply the handbrake, then shift to P, and it won't happen.

What is the RPM of the car? If the RPM is too high when the engine is cold, it will definitely jerk when you shift gears.