One advantage of the 5-Line Staff is use of both lines and spaces. It's compact, easy to print, and easy to stack notes vertically.
Another advantage: each note of a diatonic scale is mapped injectively. Cf. representing each line (or space) as a whole-tone, which leads to hash-collisions (e.g. "is that a G or a G#?"). Each note on a line (or space) on which collisions occur would need an accidental. Which defeats the purpose of key signatures.
A diatonic scale contains an odd number of unique notes. The fact that C lies on a line while C' lies on a space is an unfortunate artifact of representing a 7-note scale with alternating lines and spaces.
Another advantage: each note of a diatonic scale is mapped injectively. Cf. representing each line (or space) as a whole-tone, which leads to hash-collisions (e.g. "is that a G or a G#?"). Each note on a line (or space) on which collisions occur would need an accidental. Which defeats the purpose of key signatures.
A diatonic scale contains an odd number of unique notes. The fact that C lies on a line while C' lies on a space is an unfortunate artifact of representing a 7-note scale with alternating lines and spaces.