Rio de Janeiro
There is an expansion for 5 to 6 players, but is it possible to start LoA for the very first time with 5 or 6 players?
Do you mean without the expansion? That would be impossible, because there are only 4 heroes in the game.
Are the legends (campaigns) for the base game adapted for 5 or 6 players?
Yes. The New Heroes expansion doesn't even come with any new legend. There may be some other minor changes, but I think you basically add a figure that increases the strength of the bosses. Also, for all legends, the time trackers are shared, not individual.