Exact BL Touch kit I ordered for my 4.2.2. Ender 5 Pro.
Downloaded firmware from Creality.com, Ender series > Ender 5 Pro > Ender-5 pro 4.2.2mainboard(32bit).zip dated 28 Jan, 2021.
Copy file from Marlin2.0.1 BLtouch V1.1.1 Non-adapter board firmware named Ender-5 Pro- Marlin2.0.1 - V1.1.1 - BLTouch.bin to an SD card and power cycle the printer
Exactly how my 5 Pro 4.2.2 is sitting right now, no frills, no extras, just works.