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We present observational evidence of three massive, accreting black holes in the z = 5.0167 galaxy J0148-4214 from JWST/NIRSpec-IFU spectroscopy. The black holes are revealed through broad H α emission (FWHM = 430–2920 km/s) without a forbidden-line counterpart in the bright [O III ] doublet. Channel maps of the asymmetric central H α profile isolate two spatially distinct broad-line regions (BLRs), separated by 190 ± 40 pc, while a third BLR is found in the galaxy outskirts with a projected separation of 1.7 kpc. We discuss whether this emission could be due to supernovae, shocks, winds, or massive stars, but find the BLR origin most likely. Using single-epoch virial relations, we estimated black hole masses of log( M • / M ⊙ ) = 7.9 ± 0.4 (primary), 5.8 ± 0.5 (secondary), and 6.3 ± 0.5 (third off-nuclear). We argue that the two central black holes will likely rapidly merge, with a simple dynamical friction time estimate of the order of ≲700 Myr. Assuming that the third off-nuclear black hole is also in the process of sinking towards the centre, it will likely lead to a second merger, and we investigated the detection probability of such mergers with LISA. Alternatively, the third black hole may be the result of a previous central three-body interaction or a gravitational recoil, where our observations would provide evidence that such black holes may retain their accretion discs and BLRs even in the aftermath of such extreme dynamical interactions. The possible discovery of a black hole triplet at high redshifts, together with other recent results on distant black hole pairs, indicates that multiple massive black hole systems were likely common in the early Universe. Our results highlight the importance of IFU observations for the detection of massive black hole multiplets in distant galaxies, the progenitors of massive black hole mergers that may be detected with next-generation gravitational wave observatories.