What is the ruling on prayer and ghusl if bleeding continues for more than twenty-four days after the cessation of menstruation for five months?

What you did by performing ghusl fifteen days after seeing blood is correct, because the maximum duration of menstruation is fifteen days. Your menstrual period is your regular habit. If you do not have a regular habit, then it is what you distinguished as having the characteristic of menstrual blood. Otherwise, consider it six or seven days of menstruation, and anything beyond that is istihada (non-menstrual bleeding). Therefore, make up the prayers you missed during the period you thought was menstruation.