% Abstract (generated from the AutoScholar manuscript, 2026-10-30)
The zero forcing number $\Z(G)$ of a graph is the minimum size of a set of initially black vertices from which the colour-change rule (a black vertex with exactly one white neighbour forces that neighbour black) eventually colours the whole graph; it bounds the maximum nullity of the matrices described by $G$. For the generalized Petersen graphs $\PP{n}{k}$ the sharp values were, to our knowledge, reported for $k=2$ (with independent confirmation only for $n\le 16$), proved for $k=3$ and $k=4$ (2026), and known for $k=5$ only at $n=11$ and at $n\equiv 0\pmod{24}$. We determine $\Z(\PP{n}{5})$ for every $n\ge 11$: the values are $6,8,9,8,8,8,10,10,10,10,10,11$ for $n=11,\dots,22$, and $\Z(\PP{n}{5})=12$ for all $n\ge 23$, so the stabilization threshold is exactly $n_0=23$. The upper bound $12$ is the published $2k+2$ construction. The lower bound for all $n\ge 26$ follows the first-force boundary method of Krishnan, Ma and Zhang, adapted to $k=5$: we prove that the minimum boundary of an $18$-vertex set in $\PP{n}{5}$ is at least $12$ for every $n\ge 26$ by a column-deletion lemma that reduces the statement to the finite window $26\le n\le 154$, which is settled by $129$ unsatisfiability certificates in DRAT format, each verified by the external checker \code{drat-trim} and rebuilt from the graph definition by an independent checker. The method provably fails at $n=25$ for every parameter $p\le 24$ (two inner pentagons give an obstruction), so $n=23,24,25$ and all $n\le 22$ are settled by exhaustive enumeration with dihedral orbit reduction, cross-validated by a second, independently written enumeration based on first-force normalization (through $n=40$) and, for $n\le 23$, by DRAT-certified fort-cover refutations. We also show that the $k=4$ parameter $p=16$ cannot work for $k=5$ at any $n\ge 22$, that the certified bound has zero slack, and that a pre-registered holdout of six values of $n$ confirmed the registered conjectures. All proofs are written out; all certificates, code and a reproduction script are released.