The Tb-Dy-Ho-Er-Tm hexagonal high-entropy alloy is a physical realization of an ideal solid solution with completely random mixing of the elements on a practically undistorted lattice. It represents a magnetically concentrated system with all lattice sites occupied by localized magnetic moments and containing randomness and frustration due to chemical disorder, thus sharing properties of an ordered crystal and an amorphous glass. The influence of this crystal-glass duality on the collective magnetic state was studied by the magnetization, magnetoresistance and specific heat experiments. The magnetic ground state is temperature-dependent, forming upon cooling first a speromagnetic state, then transforming into a spin glass state, followed by another transformation into an asperomagnetic state. The observed temperature evolution of the magnetic ground state is a result of temperature-dependent, competing magnetic interactions, where the distribution of the exchange interactions shifts continuously from the high-temperature speromagnetic-type through the spin glass-type to the low-temperature asperomagnetic-type.