The skin wasn't firm, you say (5)

I believe the answer is:

suede

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'the skin' is the definition.
(suede is a kind of skin)

I cannot understand how the rest of the clue works.

(Other definitions for suede that I've seen before include "Hide from kids" , "Type of leather" , "Fabric" , "unprepared material" , "Form of leather" .)

I've seen this clue in the Evening Standard.

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