  Recently, LiGa$_5$O$_8$ was identified as a cubic spinel type
ultra-wide-band-gap semiconductor with a gap of about 5.36 eV and reported to
be unintentionally p-type. Here we present first-principles calculations of the
native defects and various of their complexes to try to explain the occurrence
of p-type doping. Although we find Li-vacancies to be somewhat shallower
acceptors than in LiGaO$_2$, and becoming slightly shallower in complexes with
donors such as V$_{\rm O}$ and Ga$_{\rm Li}$ antisites, these $V_{\rm Li}$
based defects are not sufficiently shallow to explain p-type doping. The
dominant defects are donors and in equilibrium the Fermi level would be
determined by compensation between donors and acceptors, and pinned deep in the
gap.
