Chapter 5, along with each Mission and Quest required, as well as any requirements or rewards.
Increase Contribution Level To 7000 / Go To Shopping Area - Northern Alley
Complete HQ Missions, Branch Missions, and Quests until your Contribution level reaches 7000 and you’ll receive an email from the Hero Association. Head to the Shopping Area and you’ll meet up with Mumen Rider. Head into the battle against the two toughs and take them out.
Increase Contribution Level To 9000 / Tending Shop
After the battle, continue working on HQ Missions, Branch Missions, and Quests until you reach 9000 Contribution. After you have reached 9000, pick up the Tending Shop HQ Mission from the attendant at the Information desk.
In this mission, you’ll be pitted against the leader of the gang, so either outlast him or knock him down by one health bar to end the fight.
Increase Contribution Level To 10000 / An Attack On Organized Crime
Work on HQ Missions, Branch Missions, or Quests to increase your contribution again, this time to 10000. After you reach that level, pick up An Attack On Organized Crime from Association HQ and you’ll meet up with Genos and Saitama as they are confronted by Speed-O’-Sound Sonic.
During the fight, you’ll be joined by Saitama, so fight him yourself or use Saitama to instantly bring an end to the fight and complete Chapter 5.