I want to update my iPhone 5s from iOS 9 to iOS 10, not iOS 11. Is it possible?
No, this is no longer possible. While you may have previously downloaded iOS 10, or may be able to download it through other online sources, installing it is no longer possible as Apple has stopped signing installations of iOS 10.

Typically, when a new version of iOS launches, the window for installing the previous version of iOS is about two weeks.