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Let $g$ be an affine Lie algebra with index set $I = \{0, 1, 2, \cdots , n\}$and $g^L$ be its Langlands dual. It is conjectured that for each Dynkin node $i\in I \setminus \{0\}$ the affine Lie algebra $g$ has a positive geometriccrystal whose ultra-discretization is isomorphic to the limit of certaincoherent family of perfect crystals for $g^L$. In this paper we construct apositive geometric crystal $V(D_5^{(1)})$ in the level zero fundamental spin$D_5^{(1)}$- module $W(\varpi_5)$. Then we define explicit $0$-action on thelevel $l$ known $D_5^{(1)}$- perfect crystal $B^{5, l}$ and show that $\{B^{5,l}\}_{l \geq 1}$ is a coherent family of perfect crystals with limit $B^{5,\infty}$. Finally we show that the ultra-discretization of $V(D_5^{(1)})$ isisomorphic to $B^{5, \infty}$ as crystals which proves the conjecture in thiscase.

$D_5^{(1)}$- Geometric Crystal corresponding to the Dynkin spin node $i=5$ and its ultra-discretization