5.
[tex]\it \sqrt{\overline{1ab}}\in\mathbb{N} \Rightarrow \overline{1ab}=121,\ \ 144,\ \ 169,\ \ 196.\\ \\ a<b \Rightarrow \overline{1ab}=169,\ \ \sqrt{169}=13\in\mathbb{N} \Rightarrow a=6,\ \ b=9[/tex]
