There were probably close to 100 tire companies in the 50's. Many were small regional companies, others were private label made by one of the larger manufacturers to the private labels specs. Based on the picture I would not venture a guess, but someone here may have a better idea. Well, I'll throw a name out there, Atlas! KK
I'd say the ID of the tire is 15". The inner center of the wide 5 rim is probably a 16"or larger that's been cut down and welded to 15" outer to run on some dirt track.