5 1/6 - 1 1/8 * (5/6 + 3/14)

First, we need to simplify the expression inside the parentheses:

5/6 + 3/14
= (35/42) + (9/42)
= 44/42
= 22/21

Now, substitute this value back into the original expression:

5 1/6 - 1 1/8 * 22/21

Convert 5 1/6 to an improper fraction:

5 1/6 = (6*5 + 1)/6 = 31/6

Now, convert 1 1/8 to an improper fraction:

1 1/8 = (8*1 + 1)/8 = 9/8

Substitute these values back into the expression:

31/6 - 9/8 * 22/21

Now, multiply the fractions:

31/6 - 9/8 * 22/21
= 31/6 - 198/168
= 31/6 - 198/168

Now, find a common denominator to subtract the fractions:

31/6 - 198/168 = 28/12 - 189/168
= (28*14 - 189)/84
= (392-189)/84
= 203/84

Therefore, 5 1/6 - 1 1/8 * (5/6 + 3/14) = 203/84.