My sister wants to marry the son of my paternal uncle. My brother was nursed with him, and we do not know how many nursings occurred: whether it was a more or less than five. Is it permissible for her to marry him?

If you mean that your brother and the son of your paternal uncle had been breast-fed by your paternal uncle’s wife or any woman other than your mother, then it is permissible for your sister to marry the son of your paternal uncle regardless of the number of nursings. This is because the sister of a brother-through-nursing is not considered a sister-through-nursing.

However, if you mean that the son of your paternal uncle and your brother had been breast-fed by your mother, then it is unlawful for the son of your paternal uncle to marry your sister if five satiating nursings have occurred within the first two years of the child’s life. This is because he would then be your sister’s brother-through-nursing. According tot he Shafi‘is and Hanbalis, if it is not know whether five nursings had occurred or not, it is then permissible to execute that marriage, because they maintain that the prohibition is not established until five satisfying nursings occur, and as long as there is doubt whether five nursings have taken place [it remains lawful] since what is certain (i.e. marriage) is not negated by doubt [i.e. occurrence of five nursings]. This is the opinion issued for fatwa because the matter so commonly occurs.
Allah Most High knows best.