Is it possible to upgrade the Galaxy Tab 10.1 (GT-P5113) from 4.2.2 to a higher Android version?

I have an unrooted Galaxy Tab 10.1 (GT-P5113) running Android 4.2.2

I want to upgrade the Android version there, however, I have no idea how.

Right now the tablet claims it is up-to-date, but we all know it is not - Android 4.2.2 is old.

Samsung Kies refuses to upgrade the firmware with the message "gt-p5113 does not support initialising".

Is there a way to upgrade the Android version on this tablet (while still keeping it usable, obviously) ? Preferably without rooting, but I will root it if there is no other choice.

I am OK completely resetting it.