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).

[0] https://link.springer.com/article/10.1007/s13143-021-00225-6

[1] https://climateactiontracker.org/global/temperatures/

[2] https://www.ipcc.ch/report/ar5/wg1/long-term-climate-change-...