In Career Mode, the objectives are explained in the pre-race screen. Tap on any Event poster to get extra info about the race: the type of challenge and the 4th- and 5th-Star objectives. Once an Event has been chosen and the car is selected, you will see the objectives again in the loading screen. If you are already racing, you can tap the Pause icon and you will see the 4th- and 5th-Star objectives displayed on the screen.