  Spin precession is one of the key physical effects that could unveil the
origin of the compact binaries detected by ground- and space-based
gravitational-wave (GW) detectors, and shed light on their possible formation
channels. Efficiently and accurately modeling the GW signals emitted by these
systems is crucial to extract their properties. Here, we present SEOBNRv5PHM, a
multipolar precessing-spin waveform model within the effective-one-body (EOB)
formalism for the full signal (i.e. inspiral, merger and ringdown) of binary
black holes (BBHs). In the non-precessing limit, the model reduces to
SEOBNRv5HM, which is calibrated to $442$ numerical-relativity (NR) simulations,
13 waveforms from BH perturbation theory, and non-spinning energy flux from
second-order gravitational self-force theory. We remark that SEOBNRv5PHM is not
calibrated to precessing-spin NR waveforms from the Simulating eXtreme
Spacetimes Collaboration. We validate SEOBNRv5PHM by computing the
unfaithfulness against 1543 precessing-spin NR waveforms, and find that for
99.8% (84.4%) of the cases, the maximum value, in the total mass range 20-300
$M_\odot$, is below 3% (1%). These numbers reduce to 95.3% (60.8%) when using
the previous version of the SEOBNR family, SEOBNRv4PHM, and to 78.2% (38.3%)
when using the state-of-the-art frequency-domain multipolar precessing-spin
phenomenological IMRPhenomXPHM model. Due to much better computational
efficiency of SEOBNRv5PHM compared to SEOBNRv4PHM, we are also able to perform
extensive Bayesian parameter estimation on synthetic signals and GW events
observed by LIGO-Virgo detectors. We show that SEOBNRv5PHM can be used as a
standard tool for inference analyses to extract astrophysical and cosmological
information of large catalogues of BBHs.
