This is more of a sales question than a service issue. You must go by the capacity plate. The tires should be 6" wide. Because the tires are 5" wide that are on there you need to figure out whether they should be pressed on flush with the inside, outside or halfway.
The tires can be the weakest link on a forklift truck meaning that they cause the truck to derate from its base capacity. For example, if your were to order a typical new 5000# pneumatic tire forklift truck with a triple mast that lifts 189", a hang on side shifter a solid pneumatic tires the capacity plate would read about 4600# and it would state that the truck is equipped with solid pneumatic tires. Let's say once the tires wear out you decide to change them to pneumatic tires. Then you would be changing the capacity of the truck to something like 3500# and you would need to order a new capacity plate reflecting that the truck now has pneumatic tires.
Sounds crazy but it is true. One of the things OSHA goes after most is to verify that the capacity plate matches exactly how the truck is exactly equipped.