The protagonist is a second-year high school student, who transfers to the city during the spring (around the time of the start of a new school year in Japan.) He'll move into a coffee shop owned by acquaintances of his parents.
The game starts out in Shibuya, but the stage is set in various parts of Tokyo.
This is a vague hint, but for what it's worth, the protagonist is in a situation where, if he doesn't fight, something bad will happen to him in the future. The part of the recent trailer that showed him imprisoned was a symbol for a "prison of mind".
The dungeon that was shown in the trailer was not automatically-generated, and the story will have various main places that are suitable for a challenge to a phantom thief with all kinds of stages and gimmicks. However, this doesn't mean there won't be any auto-generated elements in game.
There will be some sort of Social Link-like feature in Persona 5.
The protagonist's first exclusively usable Persona is named "Arsène". This is likely derived from the famous phantom thief, Arsène Lupin.
In previous titles, the Persona summoning scene had the Japanese onomatopoeia of "カッ" (kka) which is something often used to depict a flash or clicking sound. In Persona 5, it's "ブチッ" (buchi) which is a snapping sound (either physically or mentally).