Is ground noise really normal? If so, why?

Intermediatic, Tonearms (and the vast majority of cartridges) are indiscriminate.  You will have four wires from the headshell plug going either to a DIN plug out or some similar output plug.  If there is a DIN plug or some other similar type of termination at the back of the tonearm, all you need is a true balanced phono cable complete with XLR connectors, and you can then plug that into your Ayre.  There should be a DIN connector (or similar, but typically a DIN) at the tonearm end of the balanced cable.  The maker of the cable will have wired up that DIN plug to carry the signal in balanced mode to the XLRs.  Everything else is the same, NO re-wiring of your tonearm is needed. Get an inexpensive Audioquest or Anti-cable balanced phono cable (specify "balanced") with XLRs at one end and a female DIN plug at the other, and Bob's your uncle. (I specify those two companies only because they give good bang for buck and they can be relied upon not to sell you a single-ended cable that merely has XLR terminations.)

Ralph, First we need to determine if the OP is truly experiencing noise due to bad grounding.  I'm not sure.  But in balanced mode, I've never had any audible grounding issue, no matter how sloppy I might be with grounding the tonearm or turntable or etc.

If you truly own an Ayre P5Xe, you are missing out.  You have a true balanced phono stage, and you should be connecting your cartridge to the input in balanced mode.  To do that optimally, you want a true balanced phono cable, which is a cable that uses identical conductors for each half of the balanced signal; one conductor being connected to each "end" of the cartridge output.  Cartridges are inherently balanced devices (at least 98% of them).  The pin on your cartridge that is labeled "GD" (for ground) can actually be used to derive the negative phase of a balanced signal.  The pin labeled "hot" or "R" or "L" will then put out only the positive phase of a balanced signal.

So, basically, to convert to balanced mode all you need is a balanced phono cable with XLR termination.  You would connect the XLR to the XLR input on your Ayre phono.  This will eliminate any noise due to poor grounding, totally.  As others have correctly noted, this will not eliminate groove noise, etc, etc.  But you could say good-bye to 60Hz or 120Hz hum due to poor grounding. If that is the real source of your problem.

Now, if you tell me that your cartridge is already connected to your Ayre in true balanced mode, then I would say you do not have noise due to poor grounding.