To solve this expression, we need to follow the order of operations (PEMDAS):

Solve the multiplication and division first:
5/6 - (2/3 * 12/13) + 1 4/13 ÷ 19
5/6 - (24/39) + 1 4/13 ÷ 19
5/6 - 8/13 + 1 4/13 ÷ 19

Simplify the multiplication and division:
5/6 - 8/13 + 1 4/13 ÷ 19
5/6 - 8/13 + 17/13 ÷ 19
5/6 - 8/13 + 1

Find a common denominator and combine the fractions:
5/6 = 65/78
8/13 = 48/78
1 = 78/78

65/78 - 48/78 + 78/78
= 65/78 - 48/78 + 78/78
= (65 - 48 + 78)/78
= 95/78

Therefore, the solution to the expression is 95/78.