Go inside and take the elevator down.
In the control room, pull the lever.
The door to the right opens and you can get to the ark.
Go through the door.
Storage Container 1 is right below you.
It's at the bottom of the stairs in front of the ark.
Ark Chest 1:
Go around the ark to the back of the cave. There is Ark Chest 1.
Storage 3, Ark Chest 2:
After being in the Ark, another exit will open. Go take it. There are Storage Container 3 and Ark Chest 2.
Storage 4 and 5:
Take the stairs up and you will see the last storage containers.