Do you really need 4-5 lug? I know that an easy solution for bigger tires is using tires/rims from many of the old Craftsman tractors . I've scrapped a few and each one had 3/4" keyed shafts . As long as the backspacing is close they would mount right on .
But that is something else to think about . Is the shaft long enough to take a bigger rim/tire combo ? Looking at your pic , I'm thinking you may not be able to get a much bigger rim on there .
Btw , cool little tractor . Did you get it complete ? Those seem to be hard to come by . The one I have was missing the rear , so slapped in one from a Huffy mower . Believe they were made 70-72(?) .
Here's mine as I got ( with the new rear in it) . All original , including paint . gonna make a nice little rider for the daughter .