  Parts I-IV showed that the number of ways to place $q$ nonattacking queens or
similar chess pieces on an $n\times n$ chessboard is a quasipolynomial function
of $n$ whose coefficients are essentially polynomials in $q$. For partial
queens, which have a subset of the queen's moves, we proved complete formulas
for these counting quasipolynomials for small numbers of pieces and other
formulas for high-order coefficients of the general counting quasipolynomials.
We found some upper and lower bounds for the periods of those quasipolynomials
by calculating explicit denominators of vertices of the inside-out polytope.
  Here we discover more about the counting quasipolynomials for partial queens,
both familiar and strange, and the nightrider and its subpieces, and we compare
our results to the empirical formulas found by Kot\v{e}\v{s}ovec. We prove some
of Kot\v{e}\v{s}ovec's formulas and conjectures about the quasipolynomials and
their high-order coefficients, and in some instances go beyond them.
