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The Armorer's Cookbook 5 is one of the many Key Items found throughout Elden Ring, located at Castle Redmane in the Commoner's Quarters in Caelid.
The Armorer's Cookbook 1 is a Key Item Recipe Book that will unlock extra crafting recipes once you have obtained it.
This includes the following recipes:
You can find the Armorer's Cookbook 5 at Redmane Castle in the far southeast of Caelid, located in a Commoner's Quarters where the backdoor entrance to the castle is located.