If a 15-minute nap during the day = 90 minutes during the night...

[Citizen Bleys]

I have heard of a method where instead of sleeping at night at all, you just take 5 20-30 minute naps throughout a day, and I have also heard that if you mess up the schedule, you become incredibly tired.

Yeah, the uberman sleep schedule. It'll take about a month to get used to, but theoretically, you could claim about half of the time you spend sleeping at night back. If you sleep too much, even by five minutes, you'll slip from Stage I (REM) into Stage II sleep, where your body is generating all of those drowsiness waves that make you hate life when you wake up (waking up during Stage III or IV will totally smurf you up). The most important thing to know is that more sleep isn't necessarily better, it's the pattern that matters more.

Most people can't handle the uberman sleep schedule.

EDIT: I suck at remembering the actual names of stuff.

I think the phrase you are looking for is "polyphasic sleep"

Unfortunately, for it to work, it requires 30 minutes of sleep every 4 hours, which means it can only be done by people who don't have jobs and thus have no special need for extra waking time.

I think one of the famous old-time yanks -- Thomas Eddison? almost killed himself trying to live on a polyphasic schedule. Pretty sure it was Eddison, but my mind switches off when it comes to American history. Good thing I'm not a yank or I'd never have made it through high school.