I have the 1D IV and it was always faster than any of the 5D body's. I always contributed this to the battery power. I actually ran comparisons on the my 500mm and the 1D IV with a timer. On smaller lenses speed was never noticeable but hit rate on in focus pictures was always higher by several %.

I would expect similar for the R5 vs the 1Dx III.

However the first lens I tried on my R5 was the EF 35mm f/1.4L II. As you know the lens is great because of the critical focus between 1.4 and 2.0 and the interesting bokeh it generates. It did great for me, but I only used it a few days.

Another lens I tested on the R5 was the EF 180mm F/3.5L Macro, and I thought it was much quicker to focus than it did with the DSLR bodies. I was actually somewhat impressed. The lens had a reputation of being very slow.

So far the critical narrow DOF focus I thought has been good.

Did you compare the EF and RF 85mm on the R5?

Not to doubt what you are saying, but I would put both lenses on the R5 and do a chart test in MF wide open to make sure it isn't a lens issue.
Or even just a simple comparison of walk around shots on the R5 with the EF 85mm and an adapter.