Final Fantasy V Downloads
Sorry, we're too clean-livin' to help you find illegal ROM downloads these days. You should be able to find a version somewhere, though. You'll want RPGE's Final Fantasy V ROM, translated from Japanese.
Windows, DOS, and Linux
The two great emulators for DOS/Windows/Linux are Snes9x and ZSNES. Most people prefer ZSNES, but they are fairly equal at present. Some computers prefer one, some prefer the other. Snes9x offers smooth OpenGL and 3dfx output methods if you have compatible hardware, but the same effect occurs in ZSNES with some newer video cards.
Try them both, and make your choice. Since the emulators will be updated periodically, we link only to their homepages rather than giving direct downloads.
Other Operating Systems
Thanks to AetherKnight, we finally have a DexDrive save for Final Fantasy V. This file is just prior to Omega, with all jobs mastered and all characters at level 99. You also have 99 of all available items. Download this DexDrive save and be sure to submit new saves if you have them!