If you write 5 1/4 notes in 5/4 at a tempo of q (quarter note)=120 and write 5 8th notes in 5/8 at e(eighth note)=120, one after another would they sound the same?
If a computer plays them, they are the same. However, it may influence how a human player interprets it, even if they don't know anything about what it meant historically, because all those extra beams will make the score look thicker, less spacious, and the notes seem to be more connected. A good player should be able to find a working interpretation regardless of this but you can help them by being aware of it.
I'd say yes. For the more common signatures of 3/4 and 3/8 the difference is that the latter was used to imply a faster tempo than the former; this was before metronome marks came into common usage. Since you've specified specific tempos, you've eliminated this features.