Hi Allan, and welcome to Outdoorking. The numbers you supplied are from the cooling air cowl of the Briggs and Stratton engine, not the mower frame. Your mower may be a model 5250, 5255, 52144, 52150 or 52155 (or some other model not mentioned in the parts lists). It probably has a model identification plate on it somewhere. The engine was manufactured on 1 February, 1982.

We have some of the information you are looking for in the manuals section, but only in the form of an illustrated parts list. Here is page 9 of 12, showing the wheel drive system for the version which has tapers on the ends of the rear axles (the version with parallels on the ends of the axles uses a slightly different arrangement for tensioning the jockey pulley, which in turn applies tension to the V belt):
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As you will notice, these diagrams are not entirely easy to read, and are not intended to be workshop manuals. I suggest you look carefully at the diagram, and return with questions. You may decide to subscribe to the manuals section of the site and download the parts list.
Some of the parts lists we have, have been marked up to show the common way of referring to V belts (section and length) but unfortunately the Ranger XC list is not one of them. However you can find out what section of belt is required by measuring the pulley width. Usually a belt of a smaller section will drop to the bottom of the pulley groove, while one of a larger section will extend above the top of the groove.