Explanation:
you know, a single side cannot be longer than the other 2 sides combined.
otherwise, the triangle cannot "close".
so, it starts with 12 cannot be longer than 5 + n.
therefore, n must be at least 7.
and n cannot be longer than 5+12 = 17
7 and 17 I would normally rule out a well, because in these cases the triangle would just be a flat line, when the 3rd side is as long as the other 2 combined.
so, in reality for a real, visible triangle, the range of valid values is 8 .. 16.
that is 9 positive integer values.