We derive the full Wess-Zumino-Witten term of a gauged chiral Lagrangian in $D=4$ by starting from a pure Yang-Mills theory of gauged quark flavor in a flat, compactified $D=5$. The theory is compactified such that there exists a ${B}_{5}$ zero mode, and supplemented with quarks that are ``chirally delocalized'' with ${q}_{L}$ (${q}_{R}$) on the left (right) boundary (brane). The theory then necessarily contains a Chern-Simons term (anomaly flux) to cancel the fermionic anomalies on the boundaries. The constituent quark mass represents chiral symmetry breaking and is a bilocal operator in $D=5$ of the form: ${\overline{q}}_{L}W{q}_{R}+\mathrm{h}.\mathrm{c}$, where $W$ is the Wilson line spanning the bulk, $0\ensuremath{\le}{x}^{5}\ensuremath{\le}R$, and is interpreted as a chiral meson field, $W=\mathrm{exp}(2i\stackrel{\texttildelow{}}{\ensuremath{\pi}}/{f}_{\ensuremath{\pi}})$, where ${f}_{\ensuremath{\pi}}\ensuremath{\sim}1/R$. The quarks are integrated out, yielding a Dirac determinant which takes the form of a ``boundary term'' (anomaly flux return), and is equivalent to Bardeen's counterterm that connects consistent and covariant anomalies. The Wess-Zumino-Witten term then emerges straightforwardly, from the Yang-Mills Chern-Simons term, plus boundary term. The method is systematic and allows generalization of the Wess-Zumino-Witten term to theories of extra dimensions, and to express it in alternative and more compact forms. We give a novel form appropriate to the case of (unintegrated) massless fermions.