Here are details via Andriasang and gaf of Yakuza 5's 'Another Drama' component.
Based off the few details leaking out of Famitsu, it appears that this part of the game presents side-stories for the various main characters.
Kiryu - Taxi
Your goal in the Race Battle is to avoid other cars and construction areas and get to the goal first. You'll be able to customize your taxi, adding tires, turbos, wheels, body decals, and other items. While driving, you can drift and make use of special moves like "Explosive Race Heat Action" and "Secret Explosive Acceleration."Outside of the Race Battle, you'll also be able to drive passengers to and from their destination. Famitsu shows Kiryu in conversation with his passengers.
Saejima - Hunting
Saejima's Another Drama is described as "hunting survival." Equipped with a hunting gun, you'll need to use stealth to approach and catch beasts. You'll also be able to make use of traps to catch your prey.
Haruka - Dancing
You'll need to help Haruka out in her live performances by playing a rhythm game. This involves tapping circle, triangle, square and X buttons as they move across a cursor. Different from the Hatsune Miku series, the cursor stays in one position. Sokuho says that it looks more like the rhythm-based games in Dream Club.Outside of the rhythm game, you'll need to take part in hand shake meetings, where you use the d-pad to determine Haruka's reaction. You'll also take part in simple quiz programs, respond to magazine interviews, and make talk show appearances. These will contribute to Haruka's idol knowledge.
Shinda - Baseball
This, of course, is played like a batting mini game. As you bat, you'll learn skills, gaining the ability to make the ball slow down for instance. Shinada will also meet his former coach and will be able to strengthen his skills even further.