Hi @Kirstin2,
What I would suggest is creating a group set, called something appropriate for your class (ex: "Project 1"), this is the master container for the groups. Once you have the group set created, you can create the 5 individual groups allowing students to self-signup inside of it, and title each one of them as one of the options (you won't be able to provide project details there, but you could do that in a page or announcement). This would allow each student to select the project they wanted to work on.
From your description, it sounds like you may have already formed the groups and want the entire group of students you already set up to select a project. I don't think there is really an official workflow for that. You could perhaps try a collaboration where the students could put their group name next to a project, but that might be getting overly complicated for your students.
I hope this helps a bit, but let us know if you have further questions or if I've misunderstood your needs.
-Chris