To solve this expression, we follow the order of operations (parentheses, exponents, multiplication and division, addition and subtraction):

First, we solve the subtraction inside the parentheses:
13.25 - 8.35 = 4.9

Next, we multiply the result by 2.5:
4.9 * 2.5 = 12.25

Now, we multiply 57 by 0.5:
57 * 0.5 = 28.5

Then, we add the result to the previous multiplication:
28.5 + 12.25 = 40.75

Finally, we divide the result by 7:
40.75 / 7 = 5.82142857143

Therefore, the result of the expression 15.96 * 5 + 5.82142857143 is approximately 15.821.