These time signatures are very interesting in nature and have a very specific purpose just like most things in music.
A measure of (3/5)/4 would mean each measure contains 3/5 of a quarter note or 3 eighth note quintuplets. A simpler example is 2(1/2)/4 where where would be 2 and a half quarter notes or 5 eighth notes.
As Matthew Read pointed out in the comments a time signature of 2(1/2)/4 can be represented as 5/8, but there is much more going on. The obvious difference between the two is that in 5/8 the eighth note gets the beat and in 2(1/2)/4 the quarter note gets the beat. This may seem insignificant, but this is a huge difference. In 2(1/2)/4 a full measure does not contain a full amount of beats. It's a half beat short. This gives a very distinct feel that may be thought of as rushed or unbalanced that would not be observed in 5/8.
One good example where this type of time signature can be applied is The Ocean by Led Zepplin. The intro and transitions are typically notated as alternating measures of 4/4 and 7/8. While that notationally is correct, it does not accurately represent the feel of this section. The quarter note is always felt as the beat to and when you start back on beat one on the measure of 4/4 it feels rushed and it feels as though you're missing half of the beat. The two measures also work together very well and act as one unit thus it is valid and in some ways better to look at these two bars as one single measure of 7(1/2)/4 instead of 4/4 and 7/8.
Listen and you'll understand why this makes sense to notate it this way:
Another example on this topic is Schism by Tool. There are many different time signatures used in this song, but one section of the song the interlude can be looked at as 6(1/2)/8. The reason for this is the combination is how a combination of measures 6/8 and 7/8 are used. The measure of 6/8 does not complete the idea by itself and is only complete with the 7/8, but the measure of 7/8 cannot stand alone and is independent. It could also be looked at as 13/8, but the two measures are still somewhat independent, thus the idea of 6.5/8.
Here's an article about it from Wikipedia:
"Schism" is renowned for its use of uncommon time signatures and the
frequency of its meter changes. In one analysis of the song, the song
alters meter 47 times. The song begins with two bars of 5/4,
followed by one bar of 4/4, followed by bars of alternating 5/8 and
7/8, until the first interlude, which consists of alternating bars of
6/8 and 7/8.
The following verse exhibits a similar pattern to the first,
alternating bars of 5/8 and 7/8. The next section is bars of 6/4
followed by one bar of 11/8. This takes the song back into alternating
5/8 and 7/8. Another 6/8 and 7/8 section follows, and after this the
song goes into repeating 7/8 bars.
The middle section is subsequently introduced, consisting of three
bars of 6/8, one bar of 3/8, and one bar of 3/4 repeating several
times. At one point it interrupts with two bars of 6/8 followed by a
bar of 4/8, twice. A single bar of 4/8 is played before the meter
switches back to a set of 6/8 for two bars and 2/4 for one bar. This
repeats, setting up another section: two bars of 9/8 followed by a bar
of 10/8, that pattern again, and then a single bar of 9/8 followed by
a bar of 6/8 and then a bar of 7/8. Next is a set of two bars of 6/8
followed by a bar of 2/8 repeated four times then a single bar of 6/8.
The outro has alternating bars of 5/8 and 7/8, ending with alternating
6/8, 2/8 that one could interpret as pulsing with a 4/4 feel.
The band has referred to the time signature as 6.5/8. Although many
composers would use 13/16 instead, 6.5/8 is still a valid fractional
I also suggest listening to it to get a good idea: