EDIT: samsh5fe titlescreen is still 'Samurai Showdown V Special', maybe it's not the 'perfect edition'.
Fullname of samsh5fe is "Samurai Shodown V Special (Final Edition, location test version)", it is indeed what some people refer to as "Perfect Edition". The word "Perfect" feels kinda counterfeit though, afaik they simply removed some gameplay elements from "Samurai Shodown V Special" (probably making the game more casual in the process) to make room for a story mode.
Except if you are using a non-merged romset, you'll probably need its parent samsh5sp.
From what I understand the "Perfect" edition of the game is an emulator that runs the "Special" edition, and overlays it with new content. It isn't a self-contained ROM.
To be more precise, the commercial emulator from "Samurai Shodown Collection" uses some quirks to replace the title screen and to add an english translation to the story mode. FBNeo use the raw romset and doesn't have any of those quirks.