tire pressure\ suspension upgrade

[northwestfarmtn]

hello, i have 22x9.00 tires on my ride, i use it on the farm and the other day i hit a bump and just about flew out of the driver seat. Thats a problem. i checked my tire pressure and they were hangin around 10 on the back and 5 on the front so to me that says of corse your gonna get bounced out. i have leaf springs in the front and back so i am not sure if i air the tires up to 15-20 lbs if it will be just as bad, is a suspension upgrade what i need. with the old trucks we would take apart the leaf springs and remove every other one and put new shackles on em but i don't think thats an option here. what would you run pressure wise in a 22" tire