We present high resolution spectroscopic data of the two giant extragalactic H II regions NGC 5461 and NGC 5471 in M101, which have been obtained with the 2.1-m telescope of the Observatorio Astronómico Nacional in San Pedro Martir, Baja California. We measured the intensities of several H and He recombination lines, and of forbidden lines of a large number of ions. We calculate the physical conditions in the two nebulae with a large number of diagnostics and determine their chemical abundances by applying ionization correction factors ( icf's) to the observed ionic abundances. For NGC 5461, the icf's are based on a tailored photoionization model of the region (Luridiana & Peimbert 2001), while for NGC 5471 they are computed from those predicted by a photoionization model of NGC 2363 (Luridiana, Peimbert, & Leitherer 1999), a region which is similar to NGC 5471 in the ionization structure. For both regions, the icf's are compared to those computed following the prescriptions by Mathis & Rosa (1991). Such comparison shows large discrepancies for several elements, including nitrogen, neon, and chlorine.