。
She wanted to escape from everyday life.
Literal
She [topic-は] daily-life [from-から] wanted-to-escape.
逃げ出す is a compound verb: 逃げる ('flee, escape') + 出す ('come out'), giving the sense of 'breaking out, escaping from a confined situation.' ~たい ('want to') in past form ~たかった describes the speaker's desire (or, here, her own desire as an embedded perspective).