You have to have a license for all 5 computers. Runtime solutions are stand-alone.
What you describe will work and not encounter licensing issues--at least you won't trip error messages and the files won't crash, but it may not produce the results that you want.
What you describe puts a completely separate copy of the database on each user's computer. Any changes made to the data by one user will not be visible to any other user as each has their own copy of the data.
And runtime solutions cannot access the same hosted database as clients of that database--you'd have to use correctly licensed copies of FileMaker Pro to do that.
So this works only if the "flow" of data is one way, from your original database to the individual users. If you need to collect the data they enter into the files after the fact and merge them back into a centralized copy, that can be done, but managing multiple versions of the same record--say it was modified in different ways by two or more runtime users, is not a simple matter to deal with and fully avoidable if you host the file over a network.