I can’t imagine how much true 5axis software would cost. Being able to use it is another story.
If you can find software you could do some hd foam, wood would be a stretch I would think with any reasonable sized bit.
At this point and time, to do this at home for a reasonable amount of money is a long way off.
Pocket cnc can do 4 axis (or a true 3, I’m not sure what they call it) I believe, but adding another is extremely complicated.
We do 2.5D or 3D in two planes.
Are you sure you have to have 5 axis?