Side quests are marked on your map with large orange question marks. They are pretty hard to miss. Just make sure you visit all the restaurants in the game and choose the gossip option so all the hot spots on your map are marked for you. Once you remove the fog of war from the map you can see the question marks if you haven't taken a quest yet. Just complete 5 of them and the achievement is yours.
Many of the side quests are follow up quests to other side quests as well. I know Lestallum has a lot of chain side quests.