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Could you elaborate
As a starting point for experimentation, I use tyre pressure/bar = 1.3 × vehicle mass/kg ÷ tyre width/mm
For the above case of a 55kg rider and assuming a light unloaded 7kg bike and 28C GP4000s blowing up to 32mm on the wider rims,
1.3×62/32=2.5You then adjust for front/rear balance and for tyre construction and personal preference for ride and handling and maybe for compromise between comfort and efficiency in some circumstances. As I said, it's just a way of picking a starting point, and it's only for bicycles with tyres of essentially circular cross section and very high casing compliance.
How far under? I'm guessing 28C GP5000s on 22m rims are going to be about 32mm actual width. My bag of a fag packet calculator points to 2.5bar (35psi) for a 55kg rider as a starting point, +10% at the back and -10% at the front is not a bad place to start for balance, so 38R/32F.
I think GP5000s can be tad harsh because the casing is coarse, but it's not like there's any much better options in 28-584.
Making the wheels less stiff won't help.