I have about 5000 miles on my '22 CX5 Signature. I got the vehicle new, in late April. I never noticed it originally, but in the last 6 weeks I have noticed a slight lurch when backing out of my condo parking spot. Im going very slowly...no acceleration, basically just covering the brake while the car is in reverse. I will get these lurches, and I have to brake. I spoke to the Dealership service desk when I was getting the oil changed this week, and they suggested its the Turbo engine. I have never driven a turbo before, so have no experience. Any suggestions? Concerns?

 

I have no suggestions for you but I can share the same experience with my '21 GT Turbo purchased new in January 22. I didn't take note of the mileage reading when it happened but I would say about the same as you (10000 km +/-). Basically at a traffic light waiting for the light to turn green, foot on the brake pedal, my cx5 starts lurching as if the gas pedal is being slightly tapped to advance. I put it in neutral but the same thing happened (except the car couldn't lurch since it was on N) but I could hear the engine revving slightly as if the gas pedal was being tapped. I then put it in park, shut off the engine, started it back up and the problem was gone. This happened to me about 3 times on different occassion, always while stopped with foot on the brake pedal. I never called the dealer because it was intermittent. I now have about 19000 km and the lurching problem hasn't happened since.🤔

 

My 2021 Signature exhibits these conditions also.
In the case of the OP:
Each morning as I back out of my garage, I go between two other cars in my driveway with only inches to spare on each side, therefore I have my foot on the brake pedal the whole time. The car's throttle does surge slighty, on and off a few times. It's nothing severe, just annoying. Recently I realized that I had forgotten something at home and went back after only driving maybe a half a mile and when I backed out the 2nd time there was no throttle surging; It seems to only happen on a dead-cold engine and once the engine has run for a couple of minutes it no longer occurs. I bought the car new and this has not changed since day one. I assume it's just in the programming of the ECM; manufacturers have gone to extreme lengths to hasten the engines warmup routine to minimize emissions and that may result in some undesirable behaviors such as this.

While in traffic:
The CX-5's (at least up until model year 2021) use a cycling a/c compressor. If the A/C symbol is illuminated on the climate panel, realize that the compressor clutch is probably engaging and dis-engaging several times a minute. If you are stopped in traffic and only using just enough brake pedal force to keep the car stationary, the slight engine speed change as the a/c cycles on and off will sometimes be enough to cause the car to lurch ahead although its never really caused my vehicle to actually move; it's more of just something you feel in my case. If I use more force on the brake pedal or use the Auto Hold feature I don't really detect this RPM change. You can also see this on tach if you're in Neutral or Park. Again, I just consider this a slight annoyance; my previous car used a variable-displacement a/c compressor that did not cycle on and off thereby avoiding this condition.