Turkish Airlines Ticket Cancellation and No Refund

I purchased a flight ticket with the number TK/WJIBZC from Turkish Airlines for my mother and siblings. The flight was scheduled for 8:30, and we arrived at 7:35. They told us we were 5 minutes late, the plane doors were closed, and our ticket was canceled without a refund. We were told there was nothing they could do and were dragged from one place to another. We had to buy another ticket, and they charged us ₺5951.33 for the new ticket for the next day. This caused us to buy tickets twice and left us in a difficult situation. We chose Turkish Airlines to avoid such issues, but they caused us trouble. I am requesting a refund. The employees spoke disrespectfully and belittled us by saying 'you should have come earlier.' We have never experienced such mistreatment. I demand that our issue be resolved. I request the necessary actions to be taken.