  In this work we include black hole (BH) seeding, growth and feedback into our
semi-analytic galaxy formation model, Delphi. Our model now fully tracks the,
accretion- and merger-driven, hierarchical assembly of the dark matter halo,
baryonic and BH masses of high-redshift ($z>5$) galaxies. We use a minimal set
of mass- and $z$-independent free parameters associated with star formation and
BH growth (and feedback) and include suppressed BH growth in low-mass galaxies
to explore a number of physical scenarios including: (i) two types of BH seeds
(stellar and those from Direct Collapse BH; DCBH); (ii) the impact of
reionization feedback; and (iii) the impact of instantaneous versus delayed
galaxy mergers on the baryonic growth. While both reionization feedback and
delayed galaxy mergers have no sensible impact on the evolving ultra-violet
luminosity function, the latter limits the maximum BH masses achieved at these
high-$z$. We then use this model, baselined against all available high-$z$
galaxy and BH data-sets, to predict the LISA detectability of merger events at
$z > 5$. As expected, the merger rate is dominated by stellar BH mergers for
all scenarios and our model predicts an expected upper limit of about 20
mergers in the case of instantaneous merging and no reionization feedback over
the 4-year mission duration. Including the impact of delayed mergers and
reionization feedback reduces this to about 12 events over the same
observational time-scale.
