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The weight hierarchy of a linear [n,k;q] code C over Fq is the sequence (d1,d2,…dk ),where dris the smallest support weight of a r-dimensional subcode of C.In this paper,by using the finite projective geometry method,we research a class of weight hierarchy of linear codes with dimension 5.We find some new necessary conditions of this class.Then we divide the weight hierarchies of this class into six subclasses,and we research one subclass and determine almost all weight hierarchies of this subclass of weight hierarchies of linear codes with dimension 5.