Please recommend if it's better to run a short distance fast, or a longer distance slowly for cardio workout?

Both: Both have a place in a balanced work out. Aerobic exercise ( faster) will stimulate your heart more, longer exercises ( stamina) - will make you expend more calories and increase capacity. Per-se a cardio work out will be a "faster" run - or whatever gets your heart going.

Slowly.: work up to a full work out. At middle age one should problaby have an evaluation prior to a major change in work out. Then, gradually increase distances. We know there is a reliable reduction in diabetes and cardiac risks at 90 min per week of exercise enough to increase heart rate. Generally this is recommended as 20-30 min 3-4 a week. Not Happening With Sprints.