Ipad M5 won't stay fully shut down and keeps booting up by itself.

How exactly are you performing the shutdown process?

Try Settings > General > [scroll down to] Shut Down, then “Slide to Power Off” as directed.

ParanoiaKo wrote:

I was performing the shut down the same way you'd force restart the device: Volume up, Volume down, and then wait for the device to power off and then I'd stop holding the button as to not allow a reboot.

That explains your problem! That is an incorrect method to power off your iPad. Here is the correct method, from the iPad User Guide.

It’s great you provided all the details you did so we could diagnose your issue.

The button sequence that you are using is not used to shut-down your iPad. The sequence that you describe is used to perform a forced-restart.

While you can use the method outlined by sberman, there are to two very simple methods to turn-off your iPad without using the physical buttons of your iPad...

1) Using the Control Centre

Swipe-downwards from top-right of the iPad screen to expose the Control Centre; tap the button at top-right:

2) From iPad settings

Settings > General > Shut Down

In addition to the two easy methods outlined above, you can use Siri...

Using Siri

While Siri can be commanded to shut down your iPad, Siri must first be activated before the speaking the verbal command. To enable Siri on iPad, open the Settings app, select Apple Intelligence & Siri, then Talk & Type to Siri and select your preferred voice activation method, such as "Siri" or "Hey Siri".

To shut down an iPad using Siri, simply activate Siri and say, "Hey Siri, shut down my iPad" or "Siri, power off my iPad". Siri will ask for a confirmation, and once you confirm, the device will power off.