Yes, but not directly. Final Draft 7 / 6 / 5 can open a script created in FD9 / 8 but the script must be saved in a particular way by the FD9 / 8 user first. The FD9 / 8 user must go to File > Export (FD9) or File > Save As (FD8) and choose Final Draft 5-7 document (.fdr) as the file format.
This command will create another copy of the script that is openable by older versions of Final Draft.
FD 7 / 6 / 5 all use the same FDR file format and no file conversion or alternate saving methods between them are necessary.
FD9 / 8's FDX file format is XML and makes it possible for Final Draft to be used on mobile devices. The old FDR format cannot be used for these purposes.
NOTE: Live support for Final Draft 7 has been discontinued. You will still be able to install, activate and use FD7 on appropriate computers but email, chat and telephone support is no longer available. Live activation assistance will be available via phone (818-789-6281) and email and chat (links on the left side of this page) until June 14, 2017.