I would like to know if the formula carbon steering wheel is compatible with PS5 with an CSL elite wheel base thanks

The Formula Carbon wheel could be used on the PS5. In fact, ANY wheel can be used on the PS5, if you use a PS5 compatible wheel base.
You still should check if the particular Wheel Base and the desired Steering Wheel are compatible to each other.

The standard CSL Elite Wheel Base and CSL Elite Wheel Base V1.1 version is not PS compatible though.
There is the CSL Elite Racing Wheel - officially licenced for Playstation with the CSL Elite Wheel Base + (officially licensed for PS4) which does work on PS. But the normal version does not.

Please check which one you own. The product on the device itself should answer this question for you without a doubt!