  Using mainly numerical methods, we investigate the ground-state phase diagram
of the S=2 quantum spin chain described by $H = \sum_j (S_j^x S_{j+1}^x + S_j^y
S_{j+1}^y + \Delta S_j^z S_{j+1}^z) + D \sum_j (S_j^z)^2$, where $\Delta$
denotes the $XXZ$ anisotropy parameter of the nearest-neighbor interactions and
$D$ the on-site anisotropy parameter. We restrict ourselves to the case with
$\Delta \ge 0$ and $D \ge 0$ for simplicity. Each of the phase boundary lines
is determined by the level spectroscopy or the phenomenological renormalization
analysis of numerical results of exact-diagonalization calculations. The
resulting phase diagram on the $\Delta$-$D$ plane consists of four phases; the
XY 1 phase, the Haldane/large-$D$ phase, the intermediate-$D$ phase and the
N\'eel phase. The remarkable natures of the phase diagram are: (1) the Haldane
state and the large-$D$ state belong to the same phase; (2) there exists the
intermediate-$D$ phase which was predicted by Oshikawa in 1992; (3) the shape
of the phase diagram on the $\Delta$-$D$ plane is different from that believed
so far. We note that this is the first report of the observation of the
intermediate-$D$ phase.
