Database functional dependency BCNF help
Look up "dependency preservation".

It is a known phenomenon that when decomposing relation schemas (along some given FD), certain other FD's can become inexpressible.

In a complete logical design, they have to be reinstated as a constraint on the database.  However, normalization theory does not cover constraints.  Normalization theory deals only with relation schemas, not with constraints between them.

If you first decompose over CD->E (leaving ABCD / CDE), you can still further decompose over A->D (leaving AD / ABC / CDE), but you will now have "lost" the BE->A dependency.