conditional branches.
Alternatively, you could use one variable instead of five switches. Add 1 to the variable every time you talk to one of the key people. Have the page condition (or conditional branch) set to check if the variable is 5 or greater.
You could use self-switches so that the same person could not advance the variable more than once. Alternatively, you could just use the one variable, but have one of the events advance it by 1, the next by 2, the next by 4, the next by 8, and the last by 16. That way you could use simply use one other variable and it would be a simple operation to determine if you had already spoken to each individual key person.