  Composite Higgs models based on SU(5)/SO(5) are characterised by the presence
of custodial triplets, like the Georgi-Machacek model. We classify all the
operators giving rise to the top mass and Higgs potential in presence of
fermion partial compositeness, with top partners in two-index representations
of SU(5). A detailed study of each operator allows us to find correlations in
the couplings of Higgs and non-Higgs pseudo-Nambu-Goldstone bosons, which
depend only on one, two or three independent parameters. We also analyse the
Higgs potential, finding that a misalignment along the custodial invariant
triplet direction is forbidden by CP conservation. Avoiding custodial breaking
allows us to select a handful of feasible models, which feature universal
patterns in the scalar masses related to their transformation properties under
the custodial symmetry. Finally, we briefly study the LHC phenomenology of the
scalars, which are always below 1 TeV even for multi-TeV condensation scales,
and find promising same-sign lepton final states enriched by hard photons.
