Technically yes it doesnt exist, and formally it doesnt either because its illlogical and complicated, but the thing with music is that its based off of math and so the numbers could be right to make a five time, but again as said by this entire thread it can be written much easier many other ways. not only easier but hoe it shoild be written, there arent any benefits to a five time

And it's for this reason that it's always written 5/4, and never 4/5.

Yes, 4/5 technically exists because it's created in a sequencer. But what happens if you put it to musical notation for some reason or other (or if you're bound to)? There are no notes with a 5-count at all. There are whole notes, half notes, quarter notes, eighth notes and so on. Those are all multiples of 2 counts. And then you have the dotted half notes and so on, which are multiples of 3 counts. There is no single note in music which equals five anywhere.

So you can have anything ending with /2, /4, /8, /16, rarely /3, but NEVER /5.