5. Let $a$ and $b$ be skew lines with an angle of $30^{\circ}$ between them. Then the planes $\alpha$ and $\beta$ that satisfy the condition “$a \subseteq \alpha, b \subseteq \beta$, and $\alpha \perp \beta$” ( ).
(A) do not exist
(B) exist and are unique
(C) exist and there are exactly two pairs
(D) exist and there are infinitely many pairs
5.D.

Any plane $\alpha$ can be made through $a$, and there can be infinitely many.
Take any point $M$ on $b$, and draw a perpendicular line to plane $\alpha$ through $M$. The plane $\beta$ determined by $b$ and the perpendicular line is perpendicular to $\alpha$.