Here's the short answer to this question: everyone. If a department is starting 5S, managers and all other employees should be included. If anyone is left out, this could lead to confusion or to messes that people don't want to take ownership of.
It is possible that some people will play a bigger role in 5S than others, which is fine. There might be 5S coordinators who are in charge of installing and maintaining 5S labeling, keeping tracking of assigned tasks, or introducing new department members to the 5S system. These people will obviously spend a lot of time thinking about 5S compared to others. Everyone should think about 5S regularly, though. 5S might initially take place as an event, but ideally it becomes a part of daily work for everyone.
It's also important to remember that company leaders should participate in 5S, especially if 5S is a company-wide effort. When people see their superiors taking 5S seriously by participating in it, they'll be more likely to take it seriously, too.