What's $(1 2 3)(1 4 5)$? Everybody gives a different answer.

Question

From my calculation: $(1 4 5 2 3)$.

From Joseph Gallian's Contemporary Modern Algebra, 9th edition, page 100:

From WolframAlpha:

Answer 1

Technically, the book isn't mistaken but might be slightly misleading. The order of the permutation $(1 2 3)(1 4 5)$ is equal to the order of the permutation $(1 4 5 3 2)$, but the disjoint cycle form of $(1 2 3)(1 4 5)$ is $(1 4 5 2 3)$. Also, note that Wolframalpha permutations goes from left to right, try inputting $(1 4 5)(1 2 3)$.