。
She extended her stay by five days.
Literal
She [topic-は] stay [object-を] 5-days extended.
延ばす is the transitive 'extend, prolong, lengthen' (paired with intransitive 延びる 'be extended'). Here the period of extension 5日間 ('five days') is placed adverbially, no particle — Japanese counters and time durations often appear bare-naked in adverbial position (5日間延ばす 'extend by 5 days,' 一週間旅行する 'travel for a week'). 滞在 ('stay, sojourn') is a Sino-Japanese noun for a planned period at a location.