To solve this problem, we will first convert all mixed numbers to improper fractions.

4 2/3 = 14/3
2 1/5 = 11/5
1 1/5 = 6/5

Now, we can perform the calculations:

14/3 11/5 + 11/5 1/3 - 5 * 6/5

(154/15) + (11/15) - (30/5)

To find the common denominator, we multiply 15 (3*5) by 10, which gives us 150.

154/15 + 11/15 - 30/15

165/15 - 30/15

(165 - 30)/15

135/15

9

Therefore, 4 2/3 2 1/5 + 2 1/5 1/3 - 5 * 1 1/5 = 9.