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This book explores a five-dimensional Kaluza-Klein type cosmological model of the universe, incorporating viscous effects through a modified equation of state. By extending Einstein's theory of general relativity into higher dimensions, the study provides deeper insights into the early universe, cosmic expansion, and the role of viscosity in the evolution of the cosmos. It presents analytical solutions under various physical assumptions and examines their implications for late-time acceleration and dark energy phenomena. Rich in mathematical rigor and physical interpretation, this work is ideal for researchers and graduate students in cosmology, theoretical physics, and applied mathematics seeking to understand the complex dynamics of a universe shaped by multidimensional theories and non-ideal cosmic fluids.