  The purpose of this paper is to classify all $p$-nilpotent restricted Lie
algebras of dimension 5 over perfect fields of characteristic $p\geq 5$. Our
work builds upon the recent work of Schneider and Usefi on the classification
of $p$-nilpotent restricted Lie algebras of dimension up to 4 over perfect
fields of characteristic $p$. The method we use here to classify $p$-nilpotent
restricted Lie algebras is the analogue of Skjelbred-Sund method for
classifying nilpotent Lie algebras.
