5. As shown in Figure 3, a square piece of paper is cut into a triangle and a trapezoid. If the area ratio of the triangle to the trapezoid is $3: 5$, then their perimeter ratio is ( ).
(A) $3: 5$
(B) $4: 5$
(C)5:6
(D) $6: 7$
5.D.

Let the lower base of the trapezoid be $a$, the upper base be $b(a>b)$, the perimeter be $p$, and the two legs of the right triangle be $a$ and $a-b$, with the perimeter being $p_{1}$. Then we have
$$
a(a+b): a(a-b)=5: 3 .
$$

Thus, $b=\frac{1}{4} a$.
Let $a=4, b=1$, then
$$
p_{1}: p=(3+4+5):(1+4+4+5)=6: 7 \text {. }
$$