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We aimed to identify the variable X-ray source 3XMM J000511.8+634018, which was serendipitously discovered through routine inspections while the 3XMM catalogue was compiled. We analysed the archival XMM-Newton observation of the source, obtained BUSCA photometry in three colours, and performed optical spectroscopy with the LBT. These data were supplemented by archival observations from the Zwicky Transient Facility. Based on its optical and X-ray properties, 3XMM J000511.8+634018 is classified as a magnetic cataclysmic variable, or polar. The flux is modulated with a period of 2.22 hr (8009.1 +- 0.2 s), which we identify with the orbital period. The bright phases are highly variable in X-ray luminosity from one cycle to the next. The source shows a thermal plasma spectrum typical of polars without evidence of a luminous soft blackbody-like component. It is non-eclipsing and displays one-pole accretion. The X-ray and BUSCA light curves show a stream absorption dip, which suggests an inclination 50degr < i < 75degr. The phasing of this feature, which occurs at the end of the bright phase, requires a somewhat special accretion geometry with a stream running far around the white dwarf before it is magnetically channelled. The period of this polar falls within the period gap of the cataclysmic variables (2.15-3.18 h), but appears to fall just below the minimum period when only polars are considered.