Should I worry if my period flow has become heavier and started 5 days after finishing my last period even if taking the pill?

Can happen not norma. Yes, not normal, may be break through bleeding on the pill, or something inside your uterus like a polyp or fibroid, or endometriosis, and must make sure u are not preg, so u need to see yoru gyn for an exam, blood work and an ultrasound.
Abnormal bleeding. Abnormal bleeding can have many causes. If you aren't pregnant, start keeping a calendar of your periods, and if they continue to be abnormal then take this to a gynecologist.