KINEMATICS

It says :
X is up / down
Z is front back
Y assumed to be left right
It also seems to have another angular axis that the spindle is attached to, so is this a 5 axis machine?
Blatantly stolen from the internet:

OK, the machine in your picture has strange axis positions, does yours actual machine have the same position for X Y and Z axis?

There are several 5 axis configurations included with LinuxCNC and they also have VisMach 3D animations so you can see exactly what is moving on screen, with no machine attached, so download the LinuxCNC ISO from here
www.linuxcnc.org/iso/linuxcnc_2.9.3-amd64.hybrid.iso
Use Rufus or Balena Etcher to write it to a USB stick, then boot your PC from it (press F12 or F8 or F11 when booting to show the boot device menu and choose the USB).
In the meu, there is CNC>LinuxCNC and this will show a config picker, so browse through SIM's and start one of the several included configs with 5 axis. Enjoy playing!
This does not install it, it does not delete anything, so when done just remove the USB and use your PC as usual.