5. If two sets $M=\left\{z \left\lvert\, z=\frac{t}{1+t}+\mathrm{i} \frac{1+t}{t}\right., t \in \mathbf{R}, t \neq-1, t \neq 0\right\}, N=\{z \mid z=$ $\sqrt{2}[\cos (\arcsin t)+\mathrm{i} \cos (\arccos t)], t \in \mathbf{R},|t| \leqslant 1\}$, then the number of elements in $M \cap N$ is （）
A. 0
B. 1
C. 2
D. 4
5. The modulus of element $z_{N}$ in $N$ is $|z|=\sqrt{2}$, let $\frac{t^{2}}{(1+t)^{2}}+\frac{(1+t)^{2}}{t^{2}}=2 \Rightarrow t^{2}=(1+t)^{2} \Rightarrow t=-\frac{1}{2} \quad$ At this point, $z_{M}=-1-\mathrm{i}$. Clearly, $z_{M} \neq z_{N}$, so $|M \cap N|=0$.