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My C5 2003 automatic with a 3.15 rear ratio, when I tried to do a burnout, my tires weren’t spinning and it sounded like the tires were locking up. I have an ABS light and traction control light. I assumed it would be my abs module but I have no issues when it comes to braking.
Have you pushed and held the traction control button for 5 seconds to put it in competitive drive? That disables traction control and you should be able to do a burn out.
HTH,
Joe K
ETA: sorry that should be the active handling button.
Turn off traction control
Hit the gas while using your left foot on the brake pedal to lock the front brakes for a standing burnout. Do not just let go of the brake quickly or try to do a long roll out unless you have some practice. Do not be the guy on cars and coffee videos
If it will not do one like that then you may have some issues.