I'm focusing on clarifying this question for the 5th edition.
Due to wordings like the Bardic Inspiration, it seemed clear to me that rolls should be out in the open, they should not be hidden. However, I can also see the argument where the DM rolls in secret, but then announces a fake number (maybe he rolled a 5, but he announces he rolled a 17).
You can use your reaction to expend one of your uses of Bardic Inspiration. You can choose to use this feature after the creature makes its roll, but before the GM determines whether the Attack roll or ability check succeeds or fails.
The other question's answers seem mostly focused on 3.5e, so I'm asking for RAW guidance, are DMs supposed to roll in the open, or in secret (with fumbling if necessary)? Is this mentioned in any book?