What is the value of a 1981 nickel?

Since the early 1980s, the San Francisco mint has struck only proof versions of normal circulation coins. Your nickel was part of a sealed proof-set package that someone opened. That can happen due to theft or ignorance, among the most common reasons. The bad news is that a proof coin that has been in circulation loses any premium that it had as an untouched proof, so I'm afraid you have a very well-struck coin worth 5 cents.