Well, they most likely meant degree 5 and not 5th order, is my guess. Just to tag on to Mitchās comments, degree 5 curves are nice and smooth internally, and still tractable when point editing- but, one additional reason for degree 5 is that the minimum number of points in a degree 5 curve or surface is 6 - which means that on one of these single span curves, you can set and maintain curvature at each end of the curve (uses 3 points) without affecting the curvature at the other end.

Degree 3, also common, are similarly useful with a four-point minimum, for establishing tangency at each end independently.

Iām told by the bigger brains that odd-degree curves are mathematically more well behaved than even-degree ones, but in practice, I donāt know that it makes a lot of difference.

-Pascal