How to install Octave 5 on Ubuntu 18.04?

The latest updated release from PPA is Xenial (16.04), this explain why you get Cannot add PPA: ''This PPA does not support bionic''. error.

GNU has distributed Octave as Flatpak package, and they do offer version 5—precisely 5.1.0 → https://flathub.org/apps/details/org.octave.Octave

Install flatpak, then add flathub repository.

sudo apt-get install flatpak
flatpak remote-add --if-not-exists flathub https://flathub.org/repo/flathub.flatpakrepo

You can proceed to install Octave now.

flatpak install flathub org.octave.Octave
flatpak run org.octave.Octave