If you have 6" diameter rims, you could instal Turf tires. They're available in 13 x 6.50 x 6" or 15 x 600 x 6", although you might need to re-gear your kart to compensate.
My buddy installed the 15" tall Turfs on his racekart. Worked out fine, but the fronts hit the frame on sharp turns limiting the turning radius a bit. His front rims had a center offset, you could use front rims with more offset to help that situation if needed.
The tallest tires I've seen for 5" diameter rims were only around 11" tall.
Some racekarts have an adjustable ride-height feture. You could check to see if your frame has oval-shaped holes where the rear axle bearing cassette's bolt on. Your front spindles might have a stack of king pin spacers between the frame and spindle, you could move all of them to the top of the spindle to raise the front a bit.