Is ground noise really normal? If so, why?

Sadly, hum is quite often the norm. It does not have to be! A properly set up system can be dead quiet, where all you hear is groove noise between songs.

Hum is a system-level issue, not due to any single component (unless it’s a crappy  design). Here is some more info:

http://www.hagtech.com/pdf/eliminatingnoise.pdf

Vinyl roar? Or hum?

I'd start by checking your interconnects are making good contact with the connectors on the TT and preamp (swap them out if you have spares), also check that the TT ground connector is securely connected to the preamp.
If the hum is still there then search up 'Ground Loops', it may be worth experimenting with ganging up all the mains plugs to a single wall socket if you haven't done that already.
Other than that I'd try to locate the source of the hum by disconnecting equipment until the hum goes away. Also check to see whether you have any equipment nearby that may be emitting interference.
The TT and preamp you reference look pretty high quality and I would not expect to hear any hum at all. The link provided by @hagtech looks like a good starting point.

Further to what @pragmasi said, ensure there are no routers, cable modems, or Wi-Fi units nearby. Move them with the volume up and note the change in hum levels.

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.