Suppose I was in 15/8 meter, so compound quintuple meter. This would be a grouping of 3-3-3-3-3. But suppose instead I wanted to group my meter 5-5-5. This would not be simple or compound. I was under the impression "odd meter" was groups of 2s and 3s, so like for 7/8, we have 2-2-3 as an option. But, for this case of 5-5-5, what would the term for this in music theory be?
A little reticent to get involved here, but...
It seems that compound time only goes as far as quadruple. No idea why, surely there's nothing wrong with quintuple et al. Maybe that's as far as they counted when the 'rules' were made!
And compound must divide by three. Not really reflected in the word used, but that's another story.
Three 'beats', each subdivided into 5 can't help but work, although hardly mainstream, would be felt as pretty 'regular', although 5 is often divided itself into 2+3 or 3+2. Written down on a stave, the grouping could be self-explanatory, by use of the beams.
15/8 could of course be subdivided any old way, 4+4+4+3, for example, but that would need to be explained at the top of the sheet.