© 2020 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by "https://www.kb.se/samverkan-och-utveckling/oppen-tillgang-och-bibsamkonsortiet/bibsamkonsortiet.html"Bibsam. The fusion-evaporation reaction S32+Si28 at 125 MeV beam energy was used to populate high-spin states in the semimagic N=28 nuclei Mn53 and Fe54. With a combination of the Gammasphere spectrometer and ancillary devices including the Microball CsI(Tl) array, extensive high-spin level schemes are derived. They exhibit rotational-like collective structures and competing single-particle excitations. The experimental results are compared with predictions from shell-model calculations, for which the inclusion of isopin-symmetry-breaking terms is found to improve the description. An interpretation of the high-spin states is put forward using cranked Nilsson-Strutinsky calculations, indicative of contributions from collective excitations beyond some 8-MeV excitation energy and highlighting the importance of the g9/2 intruder orbital in this energy range.