5. Given real numbers $a, b$ satisfy $a>b>0, c$ satisfies that a triangle can be formed with $a, b, c$ as its side lengths. If the largest angle among the three interior angles of the triangle is to have the minimum value, then $c$ should be equal to ( ).
(A) $a$
(B) $\frac{a+b}{2}$
(C) $\sqrt{a b}$
(D) $b$