Provided you have appropriate tow vehicle and trailer, moving 5000 pounds is not big a deal at all. My little Tacoma is rated to pull 6500 pounds. We are missing a lot of critical details out about your situation to make a good recommendation. How far do you need to move them? What equipment do you have access to at each end? Are the plates cast or stone? What is the physical size of the plates?
The weight is not the issue, 5000 pounds is only one car or a nice boat. Any respectable backhoe can lift 2500 pounds onto your trailer. But a skid loader may be at its upper limit getting it high enough to load. Rather the sensitivity of the surface plates is the concern. I would not try to move them on the stand or mounting platform. I doubt that the mount or stand is designed for the changing loads and bumps of hauling. Strapping the plates down while on the mounts will add huge loads to the mount, in addition to the weight of the plates. If you can remove the plates without a huge effort, I would move them separate.
If you really do not want to take them apart, you should use cribbing to support the weight rather than allow the mounts to do that while traveling. OR, perhaps make a "bed" for the plate from lumber, ridged foam insulation, and a CLEAN piece of carpet. It would look like this. trailer bed, 2 x 4's face down on the bed perpendicular to frame rails spaced maybe 12" OC. 3/4 plywood screwed to the 2 x 4's to make a floor with no bumps. 1 or 2" ridged foam with a few lines of glue to hold it in place on the plywood. A piece of clean carpet over the foam. Then turn the plate face DOWN on the bed so the weight is low and the mount is not carrying the load in transit. Strap it down good.
Good Luck,
John

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