Comprobación de la duración máxima de días consecutivos que cumplen una condición específica

Esta solución parece funcionar bastante bien siempre que haya un índice compuesto en user_id y en drinks_id -

SELECT *
FROM (
    SELECT t.*, IF(@prev + INTERVAL 1 DAY = t.d, @c := @c + 1, @c := 1) AS streak, @prev := t.d
    FROM (
        SELECT DATE(timestamp) AS d, COUNT(*) AS n
        FROM beverages_log
        WHERE users_id = 1
        AND beverages_id = 1
        GROUP BY DATE(timestamp)
        HAVING COUNT(*) >= 5
    ) AS t
    INNER JOIN (SELECT @prev := NULL, @c := 1) AS vars
) AS t
ORDER BY streak DESC LIMIT 1;