To find the average of these two points, we will add the x-coordinates and y-coordinates of the two points separately and then divide by 2.

Adding the x-coordinates:
5 + 1 = 6

Dividing by 2:
6 / 2 = 3

Adding the y-coordinates:
6 - 3 1/3 + 5 + 1 1/3 = 8 2/3

Dividing by 2:
8 2/3 / 2 = 4 1/3

Therefore, the average of the two points (5,6-3 1/3) and (1,5+1 1/3) is (3, 4 1/3).