The Fifth International Conference on Applied Category Theory took place at the University of Strathclyde in Glasgow, Scotland on 18-22 July 2022. This conference follows the previous meetings at Leiden (2018), Oxford (2019), MIT (2020, fully online), and Cambridge (2021). The conference comprised 59 contributed talks, a poster session, an industry showcase session, and a session where junior researchers who had attended the Adjoint School presented the results of their research at the school. Information regarding the conference may be found at (https://msp.cis.strath.ac.uk/act2022). The contributions to ACT2022 ranged from pure to applied and included contributions in a wide range of disciplines in science and engineering. ACT2022 included talks in linguistics, functional programming, classical mechanics, quantum physics, probability theory, electrical engineering, epidemiology, thermodynamics, engineering, and logic. ACT2022 was sponsored by Huawei, Protocol Labs, Cambridge Quantum, Conexus, Topos, and SICSA (Scottish Informatics and Computer Science Alliance). Submission to ACT2022 had three tracks: extended abstracts, software demonstrations, and proceedings. The extended abstract and software demonstration submissions had a page limit of 2 pages, and the proceedings track had a page limit of 14 pages. Only papers submitted to the proceedings track were considered for publication in this volume. In total, there were 97 submissions, of which 59 were accepted for presentation and 24 for publication in this volume. Publication of accepted submissions in the proceedings was determined by personal choice of the authors and not based on quality. Each submission received a review from three different members of the programming committee, and papers were selected based on discussion and consensus by these reviewers.

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