I did some playing last night and was surprised that you can have any denominator for a time signature, so my initial idea is wrong...not that I really understand what 5/9 time would really mean, but obviously LP interprets it.
OT but entertaining:
:)
5/9 means a measure of 5 "ninth" notes, just as 5/8 means a measure of 5 "eighth" notes.
What is a ninth note?
A ninth note is a note that lasts exactly 1/9 of a whole note (just as an eighth note is a note that lasts exactly 1/8 of a whole note).
So in the figure ...
\times 8/9 { c'8 c'8 c'8 c'8 c'8 c'8 c'8 c'8 c'8 }
... each of the notes carry the (effective) duration of 1/9 of a whole note ... which makes each of the nine notes above "ninth" notes.
Now, an absolutely *remarkable* aspect of Lily's durationhandling is that the following constructions are all valid:
\times 8/9 { c'8 } % a single "ninth" note
\times 8/9 { c'8 c'8 } % a pair of ninth notes
\times 8/9 { c'8 c'8 c'8 } % three of them
\times 8/9 { c'8 c'8 c'8 c'8 } % four
\times 8/9 { c'8 c'8 c'8 c'8 c'8 } % five ninth notes
(Try it; this is one of the things that modern(ist) compers discover about Lily that works "out of the box" that absolutely amazes us; try doing this with Finale and Sibelius ... and then trying doing this with these things crossing *over* barlines ...)
So the meter 5/9 then stands for a measure of exactly five ninth notes:
\new Staff {
\time 5/9
\times 8/9 { c'8 [ c'8 c'8 c'8 c'8 ] }

\time 5/8
c'8 [ c'8 c'8 c'8 c'8 ]
}
(Notice that the bar check passes just fine showing that Lily's duration math is all caught up at the end of the first measure.)
Opinions differ as to whether the tuplet should draw over such figures; there seems, in general, to be a preference against drawing the tuplet:
\new Staff {
\time 5/9
\once \override TupletNumber #'transparent = ##t
\times 8/9 { c'8 [ c'8 c'8 c'8 c'8 ] }

\time 5/8
c'8 [ c'8 c'8 c'8 c'8 ]
}
So there's that