Deciding locants of double bonds vs. other substituents
According to the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) while numbering the parent chain, an unsaturation is preferred over a substitutent.

P-14.4 Numbering
When several structural features appear in cyclic and acylic compounds, low locants are assigned  to them in the following decreasing order of seniority.
.. (a) fixed numbering of a ring or ring system;
.. (b) heteroatoms in chains and in rings and ring systems;
.. (c) indicated hydrogen;
.. (d) principal characteristic groups and free valences (suffixes);
.. (e) added hydrogen;
.. (f) saturation/unsaturation (hydro/dehydro prefixes and ‘ene’ and ‘yne’ endings);
.. (g) detachable alphabetized prefixes, all considered together in a series of increasing numerical  order;
.. (h) lowest locants for the substituent cited first as a prefix in the name;
..

As per the preference order the ketone will get the priority first as it is the principal characteristic group. Thus the name will end in an -one.
Now as the unsaturation is preferred over a substituent the numbering will be done in such a way that the double bond gets the lower number.
Thus the preferred IUPAC name of this molecule would be (5S)-5-aminocyclohex-2-en-1-one.