Garbage left abandoned staff finally collected in interval (5)

I believe the answer is:

fifth

'interval' is the definition.
(type of musical interval)

I don't understand how the remainder of the clue works.

(Other definitions for fifth that I've seen before include "Interval of three tones and a semitone" , "US amendment guaranteeing the right to silence" , "Next after fourth" , "Musical interval" , "20 per cent" .)

I've seen this clue in The Times.

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