The Calorimetric Electron Telescope (CALET), in operation on the International Space Station since 2015, has collected a large sample of cosmic-ray charged particles and gamma-rays over a wide energy interval. The instrument consists of two layers of segmented plastic scintillators to identify the charge of individual elements from proton to iron (and above), a thin imaging tungsten scintillating fiber calorimeter providing accurate particle tracking, and a lead-tungstate homogeneous calorimeter to measure energy. One of the scientific objectives of CALET is the direct measurement of the energy spectra of cosmic nuclei conveying important information on their acceleration and propagation in the Galaxy. Based on the first five years of CALET observation, CALET has measured the iron spectrum in the range of kinetic energy per nucleon from 10 GeV/n to 2.0 TeV/n. We present the CALET iron results, describe the analysis of the data and the detailed assessment of systematic uncertainties, and compare the CALET results with the findings of previous experiments.