The electron spin resonance absorption spectrum of Eu^{2+} ions serves as a probe of the normal and superconducting state in Eu_{0.5}K_{0.5}Fe_2As_2. The spin-lattice relaxation rate 1/T_1^{\rm ESR} obtained from the ESR linewidth exhibits a Korringa-like linear increase with temperature above T_C evidencing a normal Fermi-liquid behavior. Below 45 K deviations from the Korringa-law occur which are ascribed to enhanced magnetic fluctuations within the FeAs layers upon approaching the superconducting transition. Below T_C the spin-lattice relaxation rate 1/T_1^{\rm ESR} follows a T^{1.5}-behavior without the appearance of a coherence peak. Comment: 5 pages, 5 figures