No, JIRA is "permissive" rather than restrictive. You don't take rights away from people, you give people rights to do things. If they shouldn't be able to do something, don't give them the rights.
Your system is probably set up with the defaults. The permission scheme will say "Browse project = role: users". In each project, you will almost certainly find the role of users contains "JIRA users" group. That is letting all the users who can log in get into every project.
To stop your group of 5 seeing other projects, you will need to either remove them from JIRA users (and let them log in via another group) or remove jira-users from all the projects, replacing it with a more suitable group to continue to let your other users in.
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