In 1975, Mike Leigh made five 5-minute films grouped together under the heading The Permissive Society. I watched them all in Paul Hettel's excellent Short Forms class at Columbia College, and I've never forgotten them, especially my favorite, The Birth of the 2001 FA Cup Final Goalie. The films deal with a variety of characters and situations in working and middle class Britain, but a common thread is that one character in each film is quiet and the other character is a talker with all his or her needs on display. And great news! Some nice person put them all on YouTube.
Classical dramatic structure starts with a protagonist who needs or wants something, pursues that need, is brought into conflict with an antagonist who has contrasting needs, they battle it out, the story is resolved when you can show that either a) the character got what she wanted b) the character didn't get what she wanted or c) the character got what she wanted but it turned out to be not what she *really* wanted.
Character-driven filmmaking is always about wrangling with time - how do you compress it so that you can get the most information about the characters across in the most economical way? Think of your screen character as a real being with a real life that stretches from birth to death, and then try to choose the moments that will tell you the most about who they are. These will tend to be the moments where they are pursuing their needs the hardest, and when they are brought into the most conflict with others and the world. It's something that Darren Arronofsky and writer Robert Siegel did so beautifully in The Wrestler - they selected the moments when Randy the Ram was most himself, most in pursuit of professional success, acceptance, and love. But how would you choose the right span of time for a five minute film?
Most short narrative films show one scene or one day - You might show the one day in a life of a character that would tell you what all that person's days are like. Far from the 16th, in the excellent Paris Je T'aime, is a great example of this. You might show the one day or moment in someone's life where everything changed forever, where they learned something new. Lynne Ramsay's short films, like Small Deaths or Gasman are good examples of these.
Mike Leigh solves the problem of time in a different way, using repetition. You can show months or even years of a character's life if his need is the same in every scene. See how he does it in the Birth of the 2001 FA Cup Final Goalie: