MacBook Pro HDMI not connecting to LG monitor after Tahoe update

Based on everything you have already tested, I would not buy any more cables or adapters yet. 

You have established that the M5 MacBook Pro can output HDMI to the Skyworth TV, while the LG monitor works with your older MacBooks. The next step is to determine exactly how macOS is detecting the LG.

One thing worth checking first is your macOS version. 

macOS Tahoe 26.6.2 is now the current Tahoe release, so if you are still running 26.2, it's worth installing the latest update before doing further troubleshooting. 

Apple currently lists 26.6.2 as the latest version, although Apple does not specifically state that it contains a fix for external-display problems. 

Apple: What's new in the updates for macOS Tahoe 26

With the LG connected, go to  >> System Settings >> General >> About >> System Report >> Graphics/Displays and check whether the LG 27MK400H appears there.

If it does, copy the information shown for the LG and post it here. If it does not appear, that is  also important to know.

Apple recommends using System Settings >> Displays, holding the Option key, and selecting Detect Displays when an external display isn't recognzed.

Apple also recommends disconnecting and reconnecting the display, putting the Mac to sleep and waking it, and restarting it.

Apple: If your external display is dark or low resolution

If the LG is detected, check whether macOS allows you to select 1920 × 1080 at 60 Hz, which is the monitor's native resolution.

Since the problem began after the Tahoe 26.2 update, testing the LG in Safe Mode would also be useful. 

If it works there but not during a normal startup, that would give us useful information about the cause.

Apple: Start up your Mac in safe mode

The most useful thing you can send me now is the Graphics/Displays information for the LG while it is connected.

macOS has become progressively less tolerant of video data packet loss from lower quality cables. In some cases, this means that a setup that worked fine before a macOS update stops working even though nothing about the hardware has changed. If your display is connected via HDMI, make sure the cable is labeled as ULTRA or PREMIUM and is less than 1 m in length. If your display is connected via Thunderbolt/USB-C, make sure the cable is from a reputable brand and capable if high-speed data transfer, and is less than 1 m in length (for Thunderbolt 5 cables, less than 0.5 m in length). Sounds like you've done that, as long as the cable you bought was of high quality and short enough.

See if the problem is present when you boot in safe mode. That process performs some system cleanup and clears caches, and also disables 3rd party extensions that may cause problems.

Start up your Mac in safe mode - Apple Support

If that does not correct the issue, test in a new user account. A newly-created user account will have all settings at default, and if the issue does not occur in that new account then it provides guidance on what may need to be changed to correct the issue.

Add a user or group on Mac - Apple Support

Once the testing is complete, the new account can easily be deleted.

Delete a user or group on Mac – Apple Support