Amici,
On a positive note the Fenix E05 is relatively inexpensive (in the US), so if this one turns out to be a lemon, a replacement can be picked up relatively on the cheap.. You could also reach out to the vendor directly, and see if they would exchange the broken bugger for a working replacement.
I've had no issues getting a replacement light directly from Maglite as well as Eagtac when something "goofy" caused those lights to fail in explicitly.
Cheers,
Serge