Does it matter what day I'm on?
Kind of. You can trigger most endings on any regular work day, except for two obscure ones, one of which can only be triggered on the first day and the other has to be done repeatedly until you get the ending. I'd say that if you carefully scour the floors in every single room on a regular work day you'll be able to unlock most of the endings.
I gradually believe that fifth ending must be a myth. I got four endings but there's no trace of the last one which can only be triggered on the first day, as you say. Did everybody found it yet? I really searched everywhere many many times... is it based on an item that already triggered another ending?