Is the Mk V not just a 'best of' all the previous mark series?
The Mark V is basically just a IIC+ with 3 modes, and a power amp that might sound slightly different but not by much.
In IIC+ mode, it's a IIC+ non-GEQ model (has a smaller coupling cap at the end of a lead channel for less low end), Volume at 7.75 (gain on Axe), bright cap engaged. FAT and DEEP and the Lead bright are not engaged. We can do this on the Axe IIC+ model (though I'm not sure if the C+ or C++ model was a GEQ or non-GEQ model for that detail). Also it can switch from triode to pentode on the V, which you are in pentode on the Axe unless you use the 300B tube.
In the Mark IV mode, it's a IIC+ circuit, but with the larger GEQ coupling cap and PULL DEEP engaged.
In EXTREME, I think it removes some or all of the negative feedback, so you could reduce negative feedback from the IIC+ model.
That said, The Mark V also has their clean modes (which can be found in one fender model or another depending which combination of mode and fat switch you like).
The Channel 2 is the hardest to match on the Axe. The Crunch channel is cool, and I'm sure exactly what amp it would match closest to. Edge is weird. Kind of the gain of the marhally crunch plus the skinnyness of a vox. And the Mark I mode is not really replicated in any way in the Axe, not the original Mark I.