Poems in the Han Dynasty often use swans' wandering to describe a couple's parting. This poem also has this meaning. Peacock is used to describe Lan Zhi and his wife, so as to create a lingering sad atmosphere.
Wandering in five miles means staying for a while every five miles. It's love for your partner, it's sentimental!
Flying to the southeast may be because Jiao Zhongqing hanged himself on a branch in the southeast (I guess)