1% Section: Conclusion2\section{Conclusion}\label{sec:conclusion}34We have determined $\Z(\PP{n}{5})$ for all $n\ge 11$ and proved that the stabilization threshold is $n_0=23$, closing the $k=5$ case of a problem left open by the 2026 results for $k=3,4$. The proof combines the known $2k+2$ construction, the first-force boundary method with the parameter $p=18$ (the smallest that can work, since $p=16$ provably fails for all $n\ge 22$), a column-deletion reduction to the finite window $26\le n\le 154$ settled by $129$ externally checked DRAT certificates, and exhaustive enumeration for $n\le 27$, which is unavoidable at $n=25$ where inner pentagons defeat the boundary method for every $p\le 24$. All values for $11\le n\le 48$ are fully certified with independently replayed witnesses and independently re-verified lower-bound evidence, a pre-registered holdout confirmed the registered conjectures, and a falsification campaign found no error. Code, certificates (with digests), the conjecture registry and a one-command reproduction script are released with this paper.5