  In this work we propose a practical entanglement classification scheme for
pure states of $2\times L\times M\times N\times H$, under the stochastic local
operation and classical communication (SLOCC), which generalizes the method
explored in the entanglement classification of $2\times L\times M\times N$ to
the five-partite system. The entangled states of $2\times L\times M\times
N\times H$ system are first classified into different coarse-grained standard
forms using matrix decompositions, and then fine-grained identification of two
inequivalent entangled states with the same standard form are completed by
using the matrix realignment technique. As an practical example, entanglement
classes of the five-qubit system of $2\times 2\times 2\times 2\times 2$ are
presented.
