We have developed an algorithm called Q5 for probabilistic classification of healthy vs. disease whole serum samples using mass spectrometry. The algorithm employs Principal Components Analysis (PCA) followed by Linear Discriminant Analysis (LDA) on whole spectrum Surface-Enhanced Laser Desorption/Ionization Time of Flight (SELDI-TOF) Mass Spectrometry (MS) data, and is demonstrated on four real datasets from complete, complex SELDI spectra of human blood serum. Q5 is a closed-form, exact solution to the problem of classification of complete mass spectra of a complex protein mixture. Q5 employs a probabilistic classification algorithm built upon a dimension-reduced linear discriminant analysis. Our solution is computationally efficient; it is non-iterative and computes the optimal linear discriminant using closed-form equations. The optimal discriminant is computed and verified for datasets of complete, complex SELDI spectra of human blood serum. Replicate experiments of different training/testing splits of each dataset are employed to verify robustness of the algorithm. The probabilistic classification method achieves excellent performance. We achieve sensitivity, specificity, and positive predictive values above 97% on three ovarian cancer datasets and one prostate cancer dataset. The Q5 method outperforms previous full-spectrum complex sample spectral classification techniques, and can provide clues as to the molecular identities of differentially-expressed proteins and peptides.