、。
She opened her handbag and looked for her house key, but couldn't find it.
Literal
She [topic-は] handbag [object-を] opened-and house [of-の] key [object-を] looked-for-and-saw [but-が], couldn't-find.
探してみた pairs 探す ('to search') with the auxiliary ~てみる ('try doing') — 'tried searching, gave it a search.' This adds a tentative, exploratory tone: she made the attempt without certainty of success. 見つかる ('to be found') is the intransitive partner of 見つける ('to find'); the negative 見つからなかった describes the failed-search outcome from the perspective of the item: 'wasn't found.' The clause-final が here introduces an unexpected or disappointing follow-up.