5. Let the sequence of complex numbers $\left\{z_{n}\right\}$ satisfy $z_{1}=\mathrm{i}, z_{n+1}=-z_{n}^{2}-\mathrm{i}$, then $\left|z_{200}\right|=$

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5. $\sqrt{2}$. Since the complex number sequence is $\mathrm{i},+1-\mathrm{i}, \mathrm{i},+1-\mathrm{i}, \mathrm{i},+1-\mathrm{i}, \cdots$ i.e., $z_{n+2}=z_{n}(n=2,3, \cdots)$. Therefore, $\left|z_{2000}\right|=\left|z_{2}\right|=$ $|1+1-i|=\sqrt{2}$.