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In this study,we investigate in detail the generalized Crewther Relation(GCR)between the Adler func-tion(D)and the Gross-Llewellyn Smith sum rules coefficient(CGLS)using the newly proposed single-scale ap-proach of the principle of maximum conformality(PMC).The resultant GCR is scheme-independent,with the resid-ual scale dependence due to unknown higher-order terms highly suppressed.Thus,a precise test of QCD theory without renormalization schemes and scale ambiguities can be achieved by comparing with data.Moreover,a demonstration of the scheme independence of the commensurate scale relation up to all orders is presented.Addi-tionally,for the first time,the Pade approximation approach has been adopted for estimating the unknown 5th-loop contributions from the known four-loop perturbative series.