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 $\mathit{\text{TESS}}$ photometry from Sectors 88 and 89 and archival $\mathit{\text{XMM-Newton}}$ timing data. The $\mathit{\text{TESS}}$ data show signals at the orbital frequency $\mathrm{\Omega }$, its first harmonic $2\mathrm{\Omega }$, the white-dwarf spin frequency $\omega$, and the spin–orbit beat frequency $\omega -\mathrm{\Omega }$. We measure $P_{\mathrm{o}\mathrm{r}\mathrm{b}}=5.38540_{-0.00028}^{+0.00027}$ h and $P_{\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}}=0.7015570_{-0.0000062}^{+0.0000059}$ h. The $\mathit{\text{XMM-Newton}}$ 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 $\mathit{\text{TESS}}$ modulations are associated with the Gaia counterpart despite the crowded field.