Yes and no. There IS a way to convert the files in two stages to convert them into a file format used by the latest release of FileMaker. But there have been many, many changes to how FileMaker functions. You'll need to test the converted files to see if they function correctly or if they'll need some "adjustments" to their design to fully function in FileMaker 13.
A couple of years back, I converted a complex 50+ file FMP 5.5 database to FileMaker 10. It took a number of days of testing and fixing minor issues before the new version functioned as I needed it. I then spent a considerably larger period of time merging files down to a system of less than 10 files, each with multiple tables in each file instead of the one table per file found in FileMaker 6 or earlier versions.
Here's how to convert the files:
First, you use FileMaker 11 to convert to .fp7 format, then you use Filemaker 13 to convert to .fmp12 format.
Here's a download link for a 30 day free trial copy of Filemaker 11 you can use for the first step of the conversion:
I also recommend that you read these two Knowledge Base articles on converting your files:
Converting to .fp7 format: http://help.filemaker.com/app/answers/detail/a_id/750/kw/converting
Converting to .fmp12 format: http://help.filemaker.com/app/answers/detail/a_id/10571/kw/converting
Be prepared to invest some time into testing and updating the converted files as there is a good chance that your converted files may not function perfectly. The KB articles cover many, but not all of the possible issues. Feel free to post back here with any issues you encounter that don't seem to have been covered by the KB articles.
Thank you both for the great suggestions!
All of my .fp3 applications worked great. After converting to *.fo7, I moved the tables to one file. I recreated the layouts. Imported scripts. And it all still worked. Yay.
Or, just leave it all as multi-files and it still works.