Orbital and spin periods of the intermediate polar 2PBC J0800.5-4306
2PBC J0800.5$-$4306 (Swift J0800.7$-$4309; optical counterpart Gaia DR3 5533020382479508736) is a hard-X-ray-selected cataclysmic variable whose magnetic subtype had remained uncertain. We analyse \textit{TESS} photometry from Sectors 88 and 89 and archival \textit{XMM-Newton} timing data. The \textit{TESS} data show signals at the orbital frequency $Ω$, its first harmonic $2Ω$, the white-dwarf spin frequency $ω$, and the spin--orbit beat frequency $ω-Ω$. We measure $P_{\rm orb}=5.38540^{+0.00027}_{-0.00028}$ h and $P_{\rm spin}=0.7015570^{+0.0000059}_{-0.0000062}$ h. The \textit{XMM-Newton} EPIC-pn, MOS1, and MOS2 periodograms show broad peaks near the 2525.6-s (0.701557-h) optical spin period. Together with the previously published cataclysmic variable classification and Swift/BAT hard-X-ray detection, these timing results identify 2PBC J0800.5$-$4306 as an intermediate polar. We report the first published measurements of its orbital and white-dwarf spin periods, while SPOC difference-image diagnostics and pixel-level timing tests support that the measured \textit{TESS} modulations are associated with the Gaia counterpart despite the crowded field.