Given a nodal (= reduced, connected, projective, having only ordinary double points as singularities) curve $C$ consisting of 5 $\mathbb P^1$ labeled $C_0, D_1, D_2, D_3, D_4$ such that $D_i$ intersects only $C_0$ in exactly one point $P_i$ and $P_i \neq P_j$ for $i \neq j$ transversally. The dual graph of $C$ is a cross with $C_0$ in the middle and $D_1, \ldots, D_4$ as leafs.
I want to compute the dimension dim $H^0(C, T_C)$ of the global sections of the tangent sheaf $T_C$ to $C$?