13. Given the complex number $z_{1}$ satisfies $(1+\mathrm{i}) z_{1}=-1+5 \mathrm{i}, z_{2}=a-2-\mathrm{i}$, where $\mathrm{i}$ is the imaginary unit, $a \in \mathbf{R}$. If $\left|z_{1}-\overline{z_{2}}\right|<\left|z_{1}\right|$, find the range of values for $a$.
13. $z_{1}=\frac{-1+5 \mathrm{i}}{1+\mathrm{i}}=\frac{(-1+5 \mathrm{i})(1-\mathrm{i})}{2}=\frac{-1+6 \mathrm{i}+5}{2}=2+3 \mathrm{i}$

So $|2+3 \mathrm{i}-(a-2+\mathrm{i})|<\sqrt{13},|4-a+2 \mathrm{i}|<\sqrt{13}$
Therefore $(a-4)^{2}+4<13,(a-4)^{2}<9,1<a<7$.