(1 3 4 5) means the arrangement 1-3, 3-4, 4-5, 5- 1, which is called a rotation. In the same way.

(2 5) means rotation 2-5, 5-2,

(2 1 3 4 5) means rotation 2- 1, 1-3, 3-4, 4-5, 5- 1.

(1 3 4 5)(2 5) means the product (compound) of two rotations. The left compound used here, from right to left, replaces (2 5) first and then (13 4 5). First, consider what 1 has become under the substitution, and 1 does not appear in the substitution. 1 only appears in substitution (1 3 4 5), so 1-3. Consider what 2 becomes, 2 appears in (2 5), 2-5, 5 appears in (1 3 4 5), so 5- 1, so 2-.

There are1-3,2-1,3-4,4-5,5-2 (1.345) (25).

There are also1-3,2-1,3-4,4-5,5-2 (21345).

Therefore, (1 3 4 5)(2 5)=(2 1 3 4 5)