In ff5, they use the job system from ff3j. If you are a "fighter", you can equip swords. If you are a "dragoon", you can equip spears. The "bererker" can use axes, and the "hunter" bows. Those are just some of the many jobs. If you have the job "fighter" for enough battles, you get ap after each battle, you can get the "equip swords" ability. If you change your job, you can give the "equip swords" ability to, for example, a black mage. Now, the black mage can use swords! The original characters (the ones you start with) can use any weapon, and you can change back to those at any time.