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The Slime Key is a "key" item in The Legend of Zelda: Link's Awakening. It's used to open Key Cavern, the third dungeon in Link's Awakening.
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Where to Find the Slime Key Location
See the full Kanalet Castle, Golden Leaves Locations Walkthrough for full instructions on where to find the Slime Key.
In summary, the Slime Key can be obtained by collected five Golden Leaves in Kanalet Castle, then returning them to Prince Richard next to Pothole Field. He'll then let Link access Pothole Field, where you can find the Slime Key buried beneath the owl statue. Use the Deluxe Shovel to get it out of the ground.