You are correct, the 5 degree might be a bit high in this context. It's quite possible however in SSP5-8.5 and even SSP4-7.0 from IPCC's predictions for 2100 ([0] for instance). A more conservative 2-3 degrees might be more accurate for climate pledges [1]. This is based on quite a few assumptions tho and varies between authors. 2300 projections can go up to 12 degrees in IPCC AR5 WG1, Figure 12.5 [2] (for the old RCP8.5 scenario).
How did CO2 become such a big focus?
Seemingly to detriment of all else, including persistent pollutants or neonics, etc? Like those very real problems happening today, vs 2100.