Eric M. Messner and Danny Gavigan in the Theater Alliance’s “Five Flights” Written by DCist contributor Andrej Krasnansky Adam Bock’s Five Flights centers around an unlikely plight – what to do with a dilapidated aviary. But when a father believes his wife’s soul lived in that bird’s home, the stakes for the aviary’s fate get a little bit higher. Theater Alliance’s set evokes the aviary with a nestlike web of branches and broken windows…