We have gone through the math on how much Carbon Dioxide warms the earth a dozen times on FR. basically if we doubled the CO2 we have today it warm the planet by about 1/2 a degree C.
In other words the statement that Carbon Dioxide is warming the planet 5 deg C or greater is is a false premise.
The expected warming from doubled CO2 attributable solely to CO2, with absolutely nothing else changing in the climate system, would be 1.2 degrees C. (Source: IPCC Third Assessment Report).