Yesterday, Square Enix's European branch confirmed on its official blog that the PlayStation port of Final Fantasy V will soon be available as a PSOne Classic on the European PSN. There is no release date yet, but the blog post mentions that Square Enix will provide one when it is closer to release. Unfortunately, the post was vague on whether this announcement was just for Europe or included other territories as well, but the lack of any announcements from Square Enix's North American branch indicates that Final Fantasy V may not be coming to the North American PSN any time soon.
The PlayStation version of Final Fantasy V was released in North America and Europe as part of the Final Fantasy Anthology collection. This version is a direct port of the original SNES release with the addition of two FMV cutscenes and some additional load times.