A new and distinct hybrid wine grapevine plant named ‘BN5-4, characterized by the following unique combination of characteristics: Very vigorous with extremely high disease resistance in the southeastern United States, including resistance to bacterial Pierces disease and a host of fungal diseases. Average- to high-yielding vines, with dark, purple-skinned, seeded berries. Wine from the variety may be produced to be light red with a pleasant character and low residual sugar, or with a foxy character.