Are there "established" systems where "Five Card Majors" isn't a strict rule?
When you open a five card major, you're not promising anything about the strength of your suit, you are simply telling your partner that you have five cards in that suit.  

Remember that you do not win tricks only on strength, you win them on length as well.  Even if you open a raggedy five card suit, and end up playing in it after getting you're partner's support, you will win extra tricks because no one else will have trumps after you draw them. On the other hand, if you wind up in a 4-3 fit because partner raised your four card open, things can be difficult if one of your opponents also has 4 or more trump.

Also remember that just because you can't open AKQJ of a major doesn't mean you can never mention that suit.  Open a minor, and rebid your major.  That tells your partner that you have four of the major, and if he also has four then you've found your fit.

This can be hard to swallow, so I recommend building some example hands. Give yourself five lousy trump and an opening hand, give your partner three random trump and enough to raise you to game, and see how the hand plays out with random opponent hands.  Likewise, give yourself AKQJ of a major, your partner the same three random trump and game values, and get a feel for which hands are easier and which hands are harder to play.