2 5/8 ÷ (6 ÷ 3 3/7) + 5 1/6

First, we need to simplify the division within the brackets:

6 ÷ 3 3/7
= 6 ÷ (24/7)
= 6 x 7/24
= 42/24
= 7/4

Now the expression becomes:

2 5/8 ÷ 7/4 + 5 1/6
= 21/8 ÷ 7/4 + 31/6
= (21/8) x (4/7) + 31/6
= 3/1 + 31/6
= 18/6 + 31/6
= 49/6
= 8 1/6

Therefore, 2 5/8 ÷ (6 ÷ 3 3/7) + 5 1/6 = 8 1/6.