On non-standard Einstein extensions of five dimensional nilpotent metric Lie algebras

Non-standard Einstein extensions of five-dimensional nilpotent metric Lie algebras are studied in the article. The main result is the following: if there exists a non-standard Einstein extension of a given five-dimensional nilpotent metric Lie algebra $(\frak{n},Q)$, then $\frak{n}$ has the following non-trivial bracket relations: $[X_1,X_2]=X_3$, $[X_1,X_4]=X_5,\,[X_2,X_3]=X_5$ in a basis $\{X_1, X_2, X_3,X_4,X_5\}$.