I have a note 3 since December 2013 now it has a problem it starts restarting automatically after using it for some time and sometimes immediately after unplugging the charger.
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Games run fine on note 3 5.0. like I said my partner playsgames on his note 3 on 5.0. its good phone and the specs are good and it can handle games well.
And battery life depends on how often you use your phone, my friend.The thing which absolutely made me loved this phone is its display, it is just fantastic.