On Instinct's solution tells you everything about unlocking this achievement but I wanted to warn you about something: this achievement is kind of "missable" (not really, tho).
/!\ when you end the story you won't have any survivor left at the Survivor Bulletin Board when you select another chapter or start a new run /!\
That means you must do this achievement around the sixth chapter or before (which is absolutely not hard as long as you have completed some side missions).
If you didn't unlock this achievement during your story run because you thought you would be able to unlock it during chapter select (as I did), one of the fastest way to gather 5 survivors is to start from Chapter 2 in Chapter Select and do these side missions:
Chapter 2:
-Craven Consultant (find cleaver + chainsaw)
-In The Cards (find 5 cards marked on the map)
-Darker Gods (the woman in the graveyard. When you have destroyed every sigil, go back and talk to the woman and HIT HER WITH YOUR HANDS before she kills herself with a knife, otherwise she won't be available as a survivor)
That's 3 survivors already. Now you have to follow the main mission until you get to Chapter 3.
During this chapter you'll receive the quest called "Blood Barter" when you are on your way to the police station. It's a very quick mission, you'll simply have to fight two guys. Be careful: don't kill the NPC called Jesse (the bodyguard) otherwise he won't be available as a survivor. Now end the quest and BOOM you got +2 survivors which means you have 5 now so you can use the board to claim your achievement.
Two last things:
-Tier 6 of the Life attributes is "Survivor Recovery". If you get this, your survivors will never get killed (they just go back to the safehouse if they've lost too much health).
-When a survivor is following you, enter in a vehicle and drive as far as you can from him: he will automatically go back to the safehouse.
Just two tips so that you don't bother going back to the safehouse to "recall" your survivors because you're afraid they get killed. It saves some time.