Okay, then the important question right now is do you still have your old HDD? Freelancer stores it's character data on the server, yes, but it stores it's account data locally with a registry entry.
What FAM does is access this entry and log it into a file, it also allows you to manage multiple accounts. This makes for easy swapping as well as avoiding the five character limit. If you have access to your old HDD then you should still be able to extract or save your account data.
If not then one of the server administrators will probably be able to move the characters for you, either way in future make use of FAM.