I think that SCM has a partnership with AlphaCAM. Our Morbidelli (from SCM) came with AlphaCAM as well.
As far as I know, AlphaCAM and MasterCAM are probably the biggest 5 axis woodworking specific packages out there.
I'm not familiar with any 5 axis software for cabinetmaking. There are plenty that will do what you want for 3 axis, but I doubt you'll find an automated 5 axis solution for your cabinet parts.
You probably need to research all the cabinet programs available, and see if any support 5 axis? Cabinet vision, or Top Solid are two main ones.
Even if you find a cabinet package to support 5 axis, you'll probably still need a separate 5 axis CAM package for non cabinet parts.
You might also consider Rhino and RhinoCAM or MadCAM.