I once introduced the motorhome-standard for that.
And that is that rear axle mostly gets close or even a bit over GAWR.
Then substract GAWR rear from GVWR to get the weight on the front axle, to calculate the presure for.
So for instance GAWR front your 5000 lbs and GAWR rear 9000 lbs, and GVWR of 13000 lbs the expected weight on front 13000=9000=4000 lbs on front. Your axle is 4080 lbs , so search for the GVWR and GAWR's and do this calculation to see .
The the highest load on the side is what you need for determining the pressure.
Your weightdivision L/R is 47.5/52.5% wich is pretty comon for motorhomes.
But you can probaly even add a reserve for your rightfront and still leftfront above the bumping border I determined at if real weight is 85% of weight the pressure is calculated for.
Lets do this calc for your frontaxle.
the 47.5% then is 85 % of the weight the pressure is calculated for.
Then 47.5/0.85=55,9% for wich you calculate the pressure .
Then your rightfront of 52.5% is 52.5/55.9= 93.9% of the weight the pressure is calculated for.
I call that percentage the Loadpercentage shortened L%.
So in lbs 1938/0,85=2280 lbs for wich you best calculate the pressure with my formula , or search back the loadcapacity in list of european tyre-maker.
Best not use American lists.
This still leaves a reserve for right Front of 138 lbs before tire gets overloaded and so in damage sone of above 100% L%