The earliest version you can run under OS X is version 5.5. Earlier versions will run only in the Classic environment, which is not available in OS X 10.5 and later.
You can convert the files and the process produces copies of your originals which are kept unchanged so it's "safe" in that regard.
However, there are issues where the files will convert but not perfectly and you may have to do further design modifications/adjustments to get the converted files to work correctly. Whether these adjustments are extensive or touch on just a few issues will depend on the design and complexity of your current system.
A few items to consider:
Later versions of FMP index fields slightly differently. FMP 5.5 indexes ignore spaces and punctuation while FMP 10 indexes do not. This means that text field based relationships that worked in FMP 10, may break after conversion until the records with such issues are edited.
Scripts that perform scripts in another file may fail to leave the correct window in the forground. This is easily fixed but may take a while if you have a lot of such scripts.
The external data sources in your FMP 5.5 files are very likely to be very convoluted and will be more so after conversion. They'll work but may be slow. Fortunately, you can easily find and edit these in FMP 10 where they're totally inaccessible to you in FMP 5.
Even after to "fix" everything, you'll still have a solution of many different files where a new FMP 10 solution might consist of a single file with many tables. You may find you want to either merge the files or simply rebuild your database from scratch to get everything all in one file.
For more on the conversion process see Knowledge Base Article #750
Getting a copy of FMP advanced and using it to generate database design reports will be well worth the extra $$ when converting such system.
You can download a trial copy of FMP 10 and try converting the files to see the scope of your conversion task.
Theres a utility out there for merging FMP database files, FMMigrator. I haven't used it myself, but would definitely look into it if I had to merge another complex FMP system into a single file.