How long does mild chest pain have to be before a person should start worrying? Five minutes? Ten minutes? More?

Unreliable. Duration of chest pain is unreliable. Quality, location and behavior of pain are more significant. A chest pain whose quality is new or something different to a person, occurring at the area of the breast bone, radiating to the arm, neck or jaw especially when associated with sweating, weakness or dizziness are more worrisome. At best, chest pain has to be evaluated by chest xray, ekg and enzymes.
Even lesser. If person have high risks even 1 min or less chest pain with exertion in non cardiac pt or at rest in cardiac pt pt should get work up asap.