5. Given
$$
\begin{array}{l}
\left\{(x, y) \mid(x+\sqrt{2})^{2}+y^{2}=a^{2}-3 a+2\right\} \cap \\
\left\{(x, y) \mid x^{2}+(y+\sqrt{2})^{2}<a\right\} \neq \varnothing .
\end{array}
$$

Then the range of real number $a$ is
5. (2.215 3,5.9717)