The 5000 and 5100 are action types, introduced in 1936, and used on a number of different J. Stevens No.s/Models. The 5000 had the old two-piece top-lever and spindle of the old G.S. Lewis design J. Stevens guns while the 5100 had the one-piece top-lever and spindle.
Just to be really confusing, the J. Stevens Arms & Tool Co. and the J. Stevens Arms Co. catalogs give the various firearms numbers (No. xxx). Half the time those numbers don't appear on the guns themselves and when they do, they are often prefaced with "Model."
50023 04.jpg
Model 345 01.jpg
No. 375 11.jpg