Any process that results in a change in state or activity of a cell or an organism (in terms of movement, secretion, enzyme production, gene expression, etc.) as a result of a 5-fluoro-2'-deoxyuridine stimulus. 5-fluoro-2'-deoxyuridine is a pyrimidine 2'-deoxyribonucleoside compound having 5-fluorouracil as the nucleobase; it is used to treat hepatic metastases of gastrointestinal adenocarcinomas and for palliation in malignant neoplasms of the liver and gastrointestinal tract.