According to Far Away Entertainment,
Fathom Events and Warner Bros. are partnering to present the extended editions of all three Hobbit movies. Shown over three nights, the epic Peter Jackson trilogy will be the first time the extended editions have ever been released in theatres. The films follow hobbit Bilbo Baggins (Martin Freeman), who is convinced by the wizard Gandalf the Grey (Ian McKellen) to accompany thirteen dwarves, led by Thorin Oakenshield (Richard Armitage), on a quest to reclaim the Lonely Mountain from the dragon Smaug (voiced by Benedict Cumberbatch). Also included will be an exclusive introduction by director Peter Jackson. First night showing starts Monday, October 5th, 2015 at 7:30pm local.
On the Far Away Entertainment and AMC sites The Battle of the Five Armies is listed as showing on the 13th of October, so it looks like the three films will be spread out over about a week's time.
Right now it is not known if any other chains will be screening the film(s).
It is also worth noting that the runtime for The Battle of the Five Armies is listed as exactly 3 hours. The theatrical cut ran only 2 hours and 24 minutes meaning the EE will contain 36 minutes of extra footage, far more than the 13 and 25 minutes included for An Unexpected Journey and Desolation of Smaug, respectively.
The home release for the Extended Edition of BoFA is currently set for November 3rd in the USA and November 16th in the UK.
Update August 6, 2015: In a new bulletin published by the Motion Picture Association of America The Extended Edition of The Battle of the Five Armies is listed with an R for some violence. During press rounds last year for the theatrical release PJ made several comments about how many excessively violent orc deaths were cut to keep the rating to PG-13. It now appears those clips (and possibly others) have been reinserted into the extended cut.