In most cases when using a rotary axis you are working on the Y axis centre line so the Y axis is not used.  All you need to do is put a change over relay in the step/dir lines for each axis and set an M code to swap the relay and a 4 axis will do 5 axis.  Using the SwapAxis command will use the settings for the 5 axis.

That is a very flimsy device for using in any machine it needs to be very rigid even for engraving due the length from the pivot point, it will move very easily.

That's exactly what I was thinking about less than 10 minutes ago: using the Y-axis and playing around with mechanical change over switches. 
My plates are 12 mm thick steel. The engines are Nema34 8.5 Nm.
On the other hand, you offer an electronic selection (here, I need more details).
The mechanical switch reassures my mind, although it may have a defect, in the long run...

Here is the page from the manual :-

SwapAxis

Sub SwapAxis(FirstAxis As Integer, SecondAxis As Integer)
This function swaps the STEP and DIR pins for the two specified axes. This has
precisely the same effect as changing the pin settings in Config->Ports&Pins. Note that
no other axis parameters or settings are changed. If the two specified axes have different
acceleration and velocity settings, unreliable operation will likely result. Note also that if
you exit Mach3 while the swap is in effect, the swapped pins will be written to the XML
configuration file, and the swap will still be in effect the next time you start Mach3. It is
illegal to perform two consecutive swaps, without first executing a ResetAxisSwap().
Doing so will likely result in incorrect operation.

Arguments:
FirstAxis in an Integer value that specifies the first axis to swap. 0=X, 1=Y, 2=Z,
etc.
SecondAxis in an Integer value that specifies the second axis to swap. 0=X, 1=Y,
2=Z, etc.
Return Value:
None

Buying a 5/6 axis breakout board is the best option.  Look at CNC4PC.com he has lots to choose from.

https://cnc4pc.com/motion-control/breakout-boards.html

Thank you. I don't see this command on the general window. Can I receive this documentation? Also, I can only connect 4 axes...??

 I don't understand how permutation can work with an extra axis

Right, well not having the ability to coordinate rotary motion with XYZ could be a real disadvantage, for example in some forms of gear cutting.  I sometimes use my rotary axis (driven by Mach3) for knurling, where it is definitely necessary to coordinate its motion.  If you could accept the lack of coordination then I would suggest just using a simple 2-axis controller based on GRBL rather than duplicating Windows and Mach3. 

It seems that there was a 5-axis project in Mach3 back in 2016 but I don't know what happened to it.  As far as I can see Mach3 supports up to 6 axes.  5 axis motion controllers are around and not too expensive, as are 5 axis BoBs.  I'd just "bite the bullet" and do a proper 5 axis solution.  If you do use changeover switches be careful where you put them - not on the stepper driver outputs!  Breaking the connection there when the driver is powered up can blow up the driver.

 I was planning to combine one of the xyz axes with the tilting (not the rotation axis of the part)

The 2 rotations (rotation of the platen, tilting of the plate) would not have stops.
In the GUI, I don't see a degree unit. I will therefore have to develop an abacus of motor speed versus rotations

abacus of coordinate versus rotation