5. Three people, A, B, and C, are hiking together and all want to know how far the nearest town is. A says: “At least 6 miles.” B says: “At most 5 miles.” C says: “At most 4 miles.” In fact, all three are wrong. Let $d$ represent the distance from them to the nearest town. Then $d$ belongs to the interval ( ).
(A) $(0,4)$
(B) $(4,5)$
(C) $(4,6)$
(D) $(5,6)$
(E) $(5,+\infty)$
5. D.

From the problem statement that none of the three people are correct, we know
$$
d \in (0,6) \cap (5,+\infty) \cap (4,+\infty) = (5,6)
$$