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Boolean functions play essential roles in certain symmetric cryptographic schemes and error-correcting codes. Apart from the cryptographic criteria satisfied by Boolean functions, constructions of functions with few Walsh spectral value are also of particular interests in cryptographic applications. Due to the problem that the five-value spectrum functions with duals being not basic plateaued functions remains to be answered, in this paper we intend to investigate the construction on non-basic plateaued duals of five-value spectrum functions. The issue of constructing non-basic totally disjoint spectra plateaued functions is dealt with from two aspects. We firstly address the characterization of non-basic plateaued functions corresponding to Walsh supports with unequal cardinality. Then the necessary and sufficient conditions of the spectral design of a partially non-basic five-value spectrum function are proposed. Meanwhile, we also provide the sufficient condition for constructing a valid five-value spectrum function whose duals are both defined on non-affine subspaces. Finally, the design of totally disjoint spectra functions on non-affine subspaces with equal cardinality is also studied. [ABSTRACT FROM AUTHOR]