Okay , first what Thought you had was a #37 41/2 inch spot. The 41/2 spot had many different designations depending on the mount , switch location {on light / on battery can } , switch material {hard rubber or metal } and lens retainer { inside mount wire snap ring / outside mount clamp ring with nut & screw. Your 5 3/4 light seems like an odd size being that it ends in the .75 all mine end in .50 or whole numbers , try taking out the lens and lay it and the light flat on a ruler for a more accurate measurement .
I think your light is a 5 1/2 like the large one on the bottom in this pic. which has a very heavy duty mount probably for a car or motorcycle and I haven't found any info. / model on yet. Also in the pic. the light sizes are 4 1/2 inch on the top , 4 inch visor light in the center and 5 1/2 inch on the bottom
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