5. The necessary and sufficient condition for $z_{1}, z_{2}, z_{3}$ to be collinear is:
(1) $\frac{z_{3}-z_{1}}{z_{2}-z_{1}}=t(t \in \mathbf{R})$
(2) $\arg \frac{z-z_{1}}{z_{2}-z_{1}}=0$
(3) $\lambda_{1}+\lambda_{2}$ $+\lambda_{3}=0, \lambda_{1} z_{1}+\lambda_{2} z_{2}+\lambda_{3} z_{3}=0\left(\lambda_{1}, \lambda_{2}, \lambda_{3}\right.$ not all zero $)$ are satisfied simultaneously.
A. (1)(2)
B. (1) (3)
C. (2)(3)
D. (1)(2) (3)
5. $\mathrm{D}$