Welcome to the forum.
Your Model 1905 was made between 1905 and 1941. Not many were made and they were all one variation - there were no easily discernable differences or improvements during the era of manufacture. Originally intended as the H&R "medium sized" solid frame replacement for the obsolete YOUNG AMERIC DOUBLE ACTION (medium solid frame, also),
the 1905/05 never gained much interest and not many are seen in the market. Blue finish as well as Nickel plated finish were offered with 3", 4 1/2", 5" and maybe 6" barrels, standard size or extended wrap around black hard rubber grips or checkered walnut. This model was ONLY offered in .32 S&W/.32 S&W Long. No known "spin-off" models have been seen.
Your s/n seems to be high in the series, indicating production in the mid to late 1930s - not enough info available to get any closer.
In the condition as evidenced by the pic, with blued finish and 4 1/2" barrel, your 1905 would currently sell AT RETAIL in the $140 to $170 range. It is capable of handling any current factory .32 S&W or ...LONG ammo, if in safe condition to shoot.
A Fairly scarce item.