Electroencephalography (EEG) is immediate and sensitive to neurological changes resulting from sleep stages and is considered a computing tool for understanding the association between neurological outcomes and sleep stages. EEG is expected to be an efficient approach for sleep stage prediction outside a highly equipped clinical setting compared with multimodal physiological signal-based polysomnography. This study aims to quantify the neurological EEG-biomarkers and predict five-class sleep stages using sleep EEG data. We investigated the three-channel EEG sleep recordings of 154 individuals (mean age of 53.8 ± 15.4 years) from the Haaglanden Medisch Centrum (HMC, The Hague, The Netherlands) open-access public dataset of PhysioNet. The power of fast-wave alpha, beta, and gamma rhythms decreases; and the power of slow-wave delta and theta oscillations gradually increases as sleep becomes deeper. Delta wave power ratios (DAR, DTR, and DTABR) may be considered biomarkers for their characteristics of attenuation in NREM sleep and subsequent increase in REM sleep. The overall accuracy of the C5.0, Neural Network, and CHAID machine-learning models are 91%, 89%, and 84%, respectively, for multi-class classification of the sleep stages. The EEG-based sleep stage prediction approach is expected to be utilized in a wearable sleep monitoring system.