If you look in the upper right corner of the Leve window in-game (or here on our site, here's a random example: http://ffxiv.gamerescape.com/w... ) you'll see a little plate-glass looking picture. That shows what 'Type' of levequest it is. We have a collection of all of the pictures here, with links to their corresponding Leves: http://ffxiv.gamerescape.com/w... There are multiple types per 'category' of Leve. ('Category' being Battlecraft, Tradecraft, or Fieldcraft.)
Basically, it means do 5 different types of levequests.