Install the standard Ubuntu 24.04 for Raspi 5, reboot, and then in a terminal (press Ctrl-Alt-t) issue the following commands:
sudo apt update
sudo apt upgrade
sudo apt install ubuntu-mate-desktop
Then reboot, and on the Mate boot menu, select the Mate desktop. It will be selected automatically the next time you reboot.
I have done this installation several times and it works perfectly.