Start with this knowledge base article: http://help.filemaker.com/app/answers/detail/a_id/750/kw/converting
Then you might download a trial copy of FileMaker 11 and use it to convert your 5.5 files to the new format to see what you get. You'll likely need to make some changes before it works perfectly. The conversion process leaves your original files unmodified while creating new converted copies of your files.
Since you don't describe what methods you use for back up and a "user database" it's hard to answer that part of your question.