The shaded boxes

The are only two ways and their reflections to arrange the digits a shown in the figure.

1. To place the largest two digits 4 and 5 in the shaded boxes; so that the remaining 1, 2 and 3 can be at any one of the three non-shaded boxes. Therefore, there is $3! = 6$ ways to do it. The same for the reflection, therefore, there are a total 12 ways.
2. It is obvious that 5 must be in a shaded box. We can place 4 next to 5 but it must be at the end and then 3 in another shaded box. The remaining 1 and 2 can be at any of the remaining two boxes. Therefore, there are $2! = 2$ and another 2 for the reflection, a total of 4.

Therefore a total of $12+4 = \boxed{16}$ ways.