5. Given $a=\mathrm{e}^{-2}, b=a^{a}, c=a^{a^{a}}$. Then the size relationship of $a, b, c$ is $\qquad$ .
5. $b>c>a$.
$$
\begin{array}{l}
\text { Given } a=\frac{1}{\mathrm{e}^{2}} \in(0,1) \\
\Rightarrow aa^{a^{a}} \text {. }
\end{array}
$$

Also, $a^{0}>a^{a}$, then $aa$. Therefore, $b>c>a$.