Is the first ghusl (ritual bath) valid if a drop of brown blood, connected to the white discharge, appeared after complete dryness, and must the fasting of the following five days be made up?

These secretions are "al-kudrah" (brownish or yellowish discharge). They are considered menses if they occur during the usual period [of menstruation] or are continuous with blood. They are not considered menses outside the usual period. Since they occurred outside the usual period, you are not required to perform ghusl (definition) (ritual bath) or repeat your prayers, and your fast is valid.