To solve this, we need to first convert all the mixed numbers to improper fractions.

-5 целых = -5
10 целых = 10
2/3 = 2/3
2 целых = 2

-5 + 1/3 + 3/5 + 10 + 2/3 ÷ 2 + 2/3
= -5 + 1/3 + 3/5 + 10 + 2/3 ÷ 2 + 2/3
= -15/3 + 1/3 + 3/5 + 30/3 + 2/3 ÷ 2 + 2/3
= (-15 + 1 + 18 + 30 + 2 ÷ 2 + 2)/3
= 36/3
= 12

Therefore, -5 целых 1/3 + 3/5 + 10 целых 2/3 ÷ 2 целых 2/3 = 12.