She lived there for about five years.

Literal

She [topic-は] there [in-に] about five-years lived.

約 ('approximately') is a one-character prefix slapped onto numerical expressions for rough estimates — 約5年, 約100人, 約3キロ — pronounced やく and roughly equivalent to English 'about'. ~年間 is the duration counter for years (as opposed to ~年, which can also mark a year of the calendar); the 間 ('interval') makes the year-span reading explicit. Note 住む takes に for the location of residence — に marks the place where the state of living holds, not で (which would mark the location of an action). The plain past 住んだ (the past form of 住む, a 五段 verb taking ~んだ instead of ~った after the 'mu' ending) wraps it cleanly.