To solve this expression, we first need to convert the mixed numbers to improper fractions:

3 4/5 = (5 3 + 4) / 5 = 15 + 4 / 5 = 19/5
1 1/19 = (19 1 + 1) / 19 = 19 + 1 / 19 = 20/19

Now we can plug these values into the expression:

(19/5 * 20/19 - 25/6) / 3.5

Simplify the expression:

(380/95 - 25/6) / 3.5
(380/95 - 394/95) / 3.5
(-14/95) / 3.5
-14/95 * 1/3.5
-14/332.5

Therefore, the final answer is -14/332.5.