Is it believable that Jennings, in all the time he was proprietor, never entered a room on the fifth floor, using an iron key or not knowing what type of key
was for those rooms?
Yes, both questions are believable.
We'll have to agree to disagree on this..probably for forever. I don't think there's any possibility at all that Jennings avoided going into a fifth floor room during
the eight years he ran the hotel.
Well, that was not quite what you asked. You asked whether it was believable that he did not enter a room on the fifth floor with an iron key.
I think that is believable, because in my opinion the keys were not iron, or he may have not had to open the doors himself, i.e. if he did do a tour of the hotel rooms, for instance to check on state of repair or similar, he might have had his manager with him who opened all the doors.
So taking at face value, I think it is believable that he never used an iron key to enter a fifth floor room.
He would also know what type of key was used for rooms on the respective floors.
hmm, probably, but he might have forgotten, or there might have been several sets of keys, for instance locks might have been changed over the years, leading him to mistake one set for another.
So I think it's believable that he did not necessarily know for certain at all times which keys were used where.
How did you come to the conclusion that Jennings had 'little to do with the day to day running of the hotel' ? You've said this before. Where is there
any evidence of him not being there frequently?
good question, perhaps I'm just assuming he was an absent boss because there's no evidence he was there frequently. I'll have to look up on what little we know of him. He was on the witness list, but never called, I think? So that implies he had nothing to add.
The main reason I think he had little to do with running the place is that he hired a manager? So the manager was there running the place, this to me implies the proprietor would be there less. Where is the evidence Jennings was there frequently?
P.S. Thanks for replying, boss. 
No problem!
When I studied historical methodology, a main principle was drilled my into then-supple mind: earlier is always better. We see this again and again in memoirs, where people's memories of things ten, twenty or thirty years earlier har completely wrong, when compared to original sources.
So other things being equal, a source stating in 1891 the key was brass will usually trump a source in 1901 stating the key was iron. Ten years is a long time to misremember, adjust memories and narratives etc.
It doesn't mean Jennings must be wrong, but to me, being ten years late to the party lowers his value significantly.