  We give a complete description of degenerations of $3$-dimensional nilpotent
algebras, $4$-dimensional nilpotent commutative algebras and $5$-dimensional
nilpotent anticommutative algebras over $ \mathbb C$. In particular, we correct
several mistakes from the paper `Contractions of low-dimensional nilpotent
Jordan algebras' by Ancochea Berm\'{u}dez, Fres\'{a}n and Margalef Bentabol.
