5. If a subset of $\{1,2, \cdots, 30\}$ is a triplet and the product of its three elements is a multiple of 8, it is called "interesting". Then $\{1,2, \cdots, 30\}$ has $\qquad$ interesting sets.
5.1 223.

Enumeration method.
If this set does not contain multiples of 4, then the three numbers are all even, totaling $\mathrm{C}_{8}^{3}=56$ ways.

If this set contains multiples of 4 but no multiples of 8, then classify by the number of multiples of 4, totaling
$$
C_{4}^{1}\left(C_{8}^{1} C_{15}^{1}+C_{8}^{2}\right)+C_{4}^{2} C_{23}^{1}+C_{4}^{3}=734 \text { (ways). }
$$

If this set contains multiples of 8, totaling
$$
\mathrm{C}_{3}^{1} \mathrm{C}_{27}^{2}+\mathrm{C}_{3}^{2} \mathrm{C}_{27}^{1}+\mathrm{C}_{3}^{3}=433 \text { (ways). }
$$

Therefore, the total is $56+734+433=1223$.