Ah, OK. So the nuts are actually "leadscrew nuts," and they're usually made of brass. The POM versions are used primarily to reduce squeaking/squealing, which is most often caused by misalignment and/or inadequate lubrication. They're basically a treatment for the issue but not a true cure.

The ones with the integrated spring and 2nd nut are "anti-backlash" leadscrew nuts, and are designed to eliminate any slop in the fit of the nut to the leadscrew. The brass ones will do less for sqeaking/squealing issues than the POM versions, but if you can fix the underlying alignment/lubrication issue(s), they'll last a lot longer.

The brass anti-backlash nut linked in your original post is not the correct one for an Ender 5 Plus. That one is "4 start," and the Ender 5 Plus has "2 start" leadscrews. This means that there are two separate threads running down the leadscrew, with their starting points 180 degrees offset from each other. A "4 start" leadscrew would have 4 threads with their starting points offset by 90 degrees from each other.

Finally ... if you have a Creality 2.2.1 silent board, enabling the G34 command is relatively straightforward with the following:

• 1 9MMx9MM adhesive-backed heatsink (Like these)
• Insanity Automation's Silent Board firmware with Dual-Z enabled
• Insanity Automation's screen flash file set

It's possible that you may not need the first item; some boards are coming with all 5 steppers equipped with heatsinks, but usually the rightmost one (E1) doesn't have one.

To enable Z auto-alignment:

1. Power on the printer and execute an M503 command using Pronterface, OctoPrint, or any terminal program that allows you to send GCode to the printer manually and capture its output.
2. Grab the output (copy/paste or screenshot); this will contain the settings currently stored in EEPROM and will give you a base to start from in reconfiguring the printer once you're done.
3. Flash the IA firmware.
4. Disconnect power and open the PSU/control case
5. Move one of the Z stepper cables to the E1 connector (the only connector along that edge of the board that is currently empty). It doesn't matter which of the two cables you move.
6. Recommended but optional: Verify and if needed, adjust the vRef for the E1 stepper driver. You'll need to have the printer powered up and a multimeter to check the voltage. You can also likely reduce vRef on the Z stepper driver since it's only handling one stepper motor now. Kersey has a good video on checking/adjusting vRef.
7. Flash the LCD panel using its own SD card slot (only accessible with the case open).
8. Reassemble and power up.
9. Set your Z-offset (M851 Z), extrusion (M92 E) , hotend PID (M301) and bed PID (M304); save with M500.
10. Perform a bed level using the touchscreen controls, focusing on leveling the bed front-to-back moreso than side-to-side. You'll notice that a Z auto-alignment is now performed as part of the auto-leveling process. Note that you may also have to modify your Z offset due to the flexing of the frame that is caused by moving the printer to open the PSU case.
11. Insert G34 in your start GCode, and make sure ABL is enabled with M420 S1.

From that point forward, a Z auto-alignment will occur before each print. You'll find that you will only have to level the bed rarely; usually when you've made some modification to the hotend (like replacing a nozzle or swapping in an all-metal hotend).

I reconfigured for Z auto-alignment a couple of months ago and think it's one of the best (and cheapest!) mods you can perform on an E5+.