Proof for this answer
The key is actually AE. The proof is simple, a key for definition is a minimal set of attributes whose closure contains all the attributes of the table. If you calculate the closure of A with respect to the given functional dependencies you will find:

A+ = {ABCD}


that does not contain the attribute E. So A is not a key, and E must be present in any key of R. And since: 

AE+ = {ABCDE}


then AE is a key, and it is minimal (you cannot remove any attribute from it without losing the property of determining all the other attributes of the relation).