Seriously, I have no clue if I'm doing this right. The last light purple colored quintuplet quarter note is just a reference to show you that I've equally divided a 4/4 bar into 5 quintuplet quarter notes, but only used the first 4.
In the picture, I've selected only the first 4 light green colored quintuplet quarter notes, since 4 quintuplet quarter notes complete 1 bar in 4/5. however, I have no idea if I even read the Wikipedia article correctly and if the end result matches up with what the article said. With that in mind, I tried to create 4/5 time as well as I could using FL Studio 10. This is notated in exactly the same way that one would write if one were writing the first four quarter notes of five quintuplet quarter notes.' 'Notationally, rather than using Cowell's elaborate series of notehead shapes, the same convention has been invoked as when normal tuplets are written for example, one beat in 4/5 is written as a normal quarter note, four quarter notes complete the bar, but the whole bar lasts only 4/5 of a reference whole note, and a beat 1/5 of one (or 4/5 of a normal quarter note). Here's a line of text copied from the Wikipedia page.
Irrational time signatures are time signatures that don't have a denominator to a power of 2 (E.g., 3/10, 5/6, 4/3). I'm studying time signatures: Particularly, 'Irrational' time signatures.