5、Let $a, b, c (c > a, b)$ be the lengths of the three sides of a right triangle, and the point $(m, n)$ lies on the line $a x + b y + c = 0$. Then the minimum value of $m^{2} + n^{2}$ is $\qquad$ .
5.1

Analysis: The distance from the origin to the line $d=\frac{c}{\sqrt{a^{2}+b^{2}}}$, since $c$ is the hypotenuse of a right-angled triangle, hence $d=1$, that is
$$
m^{2}+n^{2} \geq d^{2}=1 ;
$$