You can start chapter 5 via the world map for Cormyr if you have completed chapter 4 and have the chapter 5 starting entry. You can also access chapter 5 directly from the ending of chapter 4 via the final conversation of the chapter.
Please report any issues via our issue tracker system or thread on forum. The full release of chapter 5 will take place on 8/19/2019. I have added Anthology - Weapons of War Chapter 5 to the drop down.