A new long-lived isomeric state in (65)Fe has been discovered with Penning trap mass spectrometry and high-precision mass measurements of the neutron-rich isotopes (63-65)Fe and (64-66)Co have been performed with the Low-Energy Beam and Ion Trap Facility at the NSCL. For the new isomer in (65)Fe an excitation energy of 402(5) keV has been determined from the measured mass difference between the isomeric and ground states. The mass uncertainties of all isotopes have been reduced by a factor of 10-100 compared to previous results. In the case of (64)Co the previous mass value was found to deviate by about 5 standard deviations from the new measurement.