FS is possibly a Flagship file, a product that uses the same format as Ashton Tate's dBase III.
This link may help:
Open your *.FS5 file by any Hex-Editor. If the first byte is (hex) 03 or 83, it is a dBaseIII+ compatible database, fully supported by FlagShip. If the 1st byte is 04, 05, 13, 23, 33, 93, B3 it is a database with FlagShip extensions. If the first byte of *.idx is (hex) 52, it is FlagShip index. See additional details on http://www.fship.com/dbfspecs.txt. If above apply, go to http://www.fship.com/eval.html for free test version of FlagShip.
If it is a Flagship file, the documentation at the link given above states that the file format for database files (but not indexes apparently) is fully compatible with dBase III so you may be able to find software (dBase, Clipper, FoxPro, Excel et al) that can extract the data if not the index info.
They also handily detail the file format in the LNG section of their docs but dBase III format is well known so you may be able to get more information elsewhere, such as here.
If it turns out to not be a Flagship/dBase file, you'll have to do some more research. The only other thing the internet suggests is that it may be a Flight Simulator file, which seems unlikely :-)
You could try running a strings
command on the files to see if any vendor-type information shows up.
Failing that, it may be that the best solution is to contact the vendor of the management software to see if they'll part with the information. Social engineering like that may provide a quicker solution than trying to reverse engineer the format.