5. Cut a wire of length $100 \mathrm{~cm}$ into $n$ small segments $(n \geqslant 3)$, each segment no shorter than $10 \mathrm{~cm}$. If for any such cutting method, there always exist 3 small segments that can form a triangle, then the minimum value of $n$ is ().
(A) 3
(B) 4
(C) 5
(D) 6
5. (C).

If a rod is divided into 4 segments, it may not form a quadrilateral, for example, with lengths $10, 17, 28$, 45. Consider the case of dividing it into 5 segments, assuming the lengths are $a, b, c, d, e$, and $10 \leqslant a \leqslant b \leqslant c \leqslant d \leqslant e$. If no segment can form a polygon, then $a+b \leqslant c, b+c \leqslant d, c+d \leqslant e$. Thus, $a+b+c+d+e \geqslant 12a \geqslant 120$, which is a contradiction. Therefore, the answer is (C).