Ok I found a solution that worked for me and I'm going to share it for the benefit of others.
On the creality3dofficial.com website I found a link on the page of the silent main board v4.2.7 upgrade kit that took me to a well buried page with binary firmwares for Ender 3 and Ender 5 printers (https://www.creality3dofficial.com/pages/ender-series).
They're not the most recent versions available on their main web site but, using the one from there (Ender-5_32bit_4.2.2_BLTouch_Marlin2.0.1 - V1.1.1), everything seems to be working as expected for me: no beeping and the BLTouch seems to be doing its job.
There are also verions fo the board V4.2.7 and for the 8bit boards for both the Ender 3 and Ender 5 printers.
Now I wonder: is it so difficult for the guys at Creality to keep a single repository of binary firmwares on their main website that keeps ALL the versions (both old and new) ever released for their printers so that we can roll back to an older version if the new one has issues?
All the best to you all.