The only thing I can think of that comes near your requirements is "dearth," ... are you sure it is five letters?
its DERTH....though i guess it is derived from dearth
Derth (5 letters)
Dearth (6 letters)
Either spelling is correct. Derth would be the answer to your question.
shortage, lack, dearth, insufficiency, scarceness, paucity, inadequacy, rarity, uncommonness, infrequency, lack, want, absence
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