Mars Golden Chest #1: Choose to patrol Mars and follow the dirt road to the right; the first building protected by enemies will have the first golden chest.
Mars Golden Chest #2: Choose to patrol Mars and go straight ahead. Down in the broken building and right before the exit is the second golden chest.
Mars Golden Chest #3: Late in The Buried City mission, you'll come to an office complex. The golden chest is in a back corner behind a desk.
Mars Golden Chest #4: At the end of The Garden's Spire mission, way up high above the gate in the final chamber is the fourth golden chest.
Mars Golden Chest #5: During A Rising Tide, after the Tharsis Junction popup, you will enter a train station filled with enemies. At the back wall is a little room with the final chest behind a corner.