Shorter than accepted answer, same idea:
(SELECT TRIM('2016-01-05' + INTERVAL a + b DAY) date
FROM
(SELECT 0 a UNION SELECT 1 a UNION SELECT 2 UNION SELECT 3
UNION SELECT 4 UNION SELECT 5 UNION SELECT 6 UNION SELECT 7
UNION SELECT 8 UNION SELECT 9 ) d,
(SELECT 0 b UNION SELECT 10 UNION SELECT 20
UNION SELECT 30 UNION SELECT 40) m
WHERE '2016-01-05' + INTERVAL a + b DAY <= '2016-01-21')