What does it mean when it says the license allows up to 5 domains but only one server? Are the 5 domains all supposed to be on the same server?

Yes you are correct, for example Form Processor Pro Business License allows up to 5 domains but only one server.

So you can install Form Processor Pro on 5 sites, but only if they are on 1 physical server (1 hosting account).

World Wide License allows to install Form Processor Pro on unlimited domains on up to 10 servers (owned by your company).

So if you need Form Processor Pro on many servers (different hosting accounts) you will need World Wide License.

If you are planning to install Form Processor Pro for your clients you will need ISP license. Reselling of product is not allowed.