We have performed a series of magnetic aging experiments on single crystals of Dy(0.5)Sr(0.5)MnO(3). The results demonstrate striking memory and chaos-like effects in this insulating half-doped perovskite manganite and suggest the existence of strong magnetic relaxation mechanisms of a clustered magnetic state. The spin-glass-like state established below a temperature T(sg)≈ 34 K originates from quenched disorder arising due to the ionic-radii mismatch at the rare earth site. However, deviations from the typical behavior seen in canonical spin glass materials are observed which indicate that the glassy magnetic properties are due to cooperative and frustrated dynamics in a heterogeneous or clustered magnetic state. In particular, the microscopic spin flip time obtained from dynamical scaling near the spin glass freezing temperature is four orders of magnitude larger than microscopic times found in atomic spin glasses. The magnetic viscosity deduced from the time dependence of the zero-field-cooled magnetization exhibits a peak at a temperature T < T(sg) and displays a marked dependence on waiting time in zero field.