  We study an AFM Heisenberg S=2 quantum spin chain at T=0 with both
interaction and on-site anisotropy, H = \sum_{i}
{1/2}(S^{+}_{i}S^{-}_{i+1}+S^{-}_{i}S^{+}_{i+1})
+J^{z}S^{z}_{i}S^{z}_{i+1}+D(S^{z}_{i})^{2}. Contradictory scenarios exist for
the S=2 anisotropic phase diagram, implying different mechanisms of the
emergence of the classical limit. One main AKLT-based scenario predicts the
emergence of a cascade of phase transitions not seen in the S=1 case. Another
scenario is in favor of an almost classical phase diagram for S=2; the S=1 case
then is very special with its dominant quantum effects. Numerical studies have
not been conclusive. Using the DMRG, the existence of hidden topological order
in the anisotropic S=2 chain is examined, as it distinguishes between the
proposed scenarios. We show that the topological order is zero in the
thermodynamical limit in all disordered phases, in particular in the new phase
interposed between the Haldane and large-$D$ phases. This excludes the
AKLT-model based scenario in favor of an almost classical phase diagram for the
$S\leq 2$ spin chains.
