Is fasting the first ten days of Ramadan valid, given that the menstrual period was interspersed with brown discharge for 15 days, of which 5 days were a normal period and the rest was dark brown discharge, and I performed ghusl and fasted on the third day of Ramadan and used to perform wudu for every prayer?

Brown discharge (kudrah) during the menstrual period is considered menstruation. If it continues for fifteen consecutive days, connected to the natural cycle, then the woman is considered to be menstruating throughout this entire period. Her fasting is not valid during this time, and she must make up the days she fasted. However, the return of blood after the fifteenth day is considered irregular bleeding (istihadah (definition)), not menstruation, and it does not prevent fasting or prayer.