5. On a long stick, there are three types of graduation lines. The first type divides the stick into 10 equal parts;

The second type divides the stick into 12 equal parts; The third type divides the stick into 15 equal parts. If each graduation line cuts the stick, how many pieces will the stick be cut into?
5. 28
5. 30 【Solution】The least common multiple of 10, 12, and 15 is 60. Taking $\frac{1}{60}$ of the length of the stick as a unit, each 10th part of the stick is 6 units long; each 12th part is 5 units long; and each 15th part is 4 units long.
Excluding the two endpoints of the stick, the internal division points of the stick are 9, 11, and 14 (corresponding to 10, 12, and 15 divisions), totaling 34.

Since the least common multiple of 5 and 6 is 30, the division points of the 10 and 12 divisions coincide at 30 units, so 1 must be subtracted from 34.

Since the least common multiple of 4 and 5 is 20, the division points of the 12 and 15 divisions coincide at 20 and 40 units, so 2 must be subtracted.

Similarly, since the least common multiple of 6 and 4 is 12, the division points of the 15 and 10 divisions coincide at 12, 24, 36, and 48 units, so 4 must be subtracted.

Since these coinciding points are all different, 1 is subtracted from 34, then 2, and then 4, resulting in 27 division points. Cutting the stick along these division points results in 28 segments.