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5. A singer pays zero rent -- crazy, eh! (5)

The word "crazy" might alert you to look for an "anagram clue" and you will know that you need to find a five letter sequence that can be rearranged to make a new word.

If you read "zero" as meaning the letter "o" you have a five letter sequence -- o,r,e,n,t -- which can be rearranged to spell a word meaning "a singer" -- "tenor".