Do I have to perform the prayer before my monthly menses, as the monthly periods after taking birth control pills are as follows:
From three days to five days: they are only very small drops (of blood), and then I have menses for seven complete days, so it is twelve or thirteen days in total.
The question is: What is the ruling on the first five days, are they considered bleeding outside the monthly periods, and is it permissible for me to perform the prayer during these days?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

If more than fifteen days elapse from the last monthly periods, and you see bleedings again, then the blood which you see now is menses whether that is due to the pills or it is your usual menses. Because if fifteen days elapse after your menses, and then you see bleedings, then it might be bleeding in advance because of the pills, so if you have these blood discharges, then it is menses, in this case you are obliged to abandon the prayer and fasting and all other prohibitions you are not allowed to do during this period that you mentioned, as long as this bleeding does not exceed fifteen days. However, if the bleeding exceeds fifteen days then you are obliged to perform Ghusl (ritual bath) and perform the prayer, as in this case it is bleeding outside your monthly menses. The fact that the quantity of blood is small does not matter; since the duration of bleeding does not exceed twelve or thirteen days, then all these days are considered your monthly menses.