This is not hard to obtain, but if you play the game without the video guide, you should restart some case.In my opinion, you must play the first run to discover the story and after restart the last case without five stars.
Drive carefully, cause if your car is too damaged, you can loose 1,2 stars.There is no stars in the last mission "A different kind of war"
It's also a way easy to unlock the trophy Traffic desk : -The Driver's Seat
-A Marriage Made In Heaven
-The Fallen Idol Homicide desk :-The Red Lipstick Murder
-The Golden Butterfly
-The Silk Stock Murder
-The White Shoe Slaying
-The Studio Secretary Murder
-The Quarter Moons Murder Vice desk : -The Black Caesar
-The Set Up
-Manifest Destiny Arson desk : The Gas Man
A Walk In Elysian Fields
House of Sticks
A Polite Invitation
Video (credit to: The red dragon