We report on the observation of high-T_c superconductivity (SC) emerging with the background of an antiferromagnetic (AFM) order in the five-layered cuprate Ba_2Ca_4Cu_5O_10(F,O)_2 through 19F-NMR and zero-field Cu-NMR studies. The measurements of spectrum and nuclear spin-lattice relaxation rates 19(1/T_1) of 19F-NMR give convincing evidence for the AFM order taking place below T_N = 175 K and for the onset of SC below T_c = 52 K, hence both coexisting. The zero-field Cu-NMR study has revealed that AFM moments at Cu sites are 0.14 mu_B at outer CuO_2 layers and 0.20 mu_B at inner ones. We remark that an intimate coupling exists between the AFM state and the SC order parameter below T_c = 52 K; the spin alignment in the AFM state is presumably changed in the SC-AFM mixed state.