#### Answer

10 ways

#### Work Step by Step

We have 5 different people, and we need to select 2 speakers for an event.
For convenience, we'll refer to those people as A, B, C, D and E.
If we select A, we can select either B, C, D or E to go as well, which means that there are 4 ways to select the members so that A goes.
If we don't select A, and we select B, we can select C, D or E to go as well, which means that there are 3 ways to select the members so that A doesn't go and B goes.
If neither A nor B goes, we can pair C and D, C and E or D and E, giving us the last 3 ways.
This gives us a total of $4+3+3=10$ ways to select the speakers.