Step 1 :The integral can be simplified by dividing the numerator by the denominator, which results in a polynomial. The integral of a polynomial can be easily calculated.
Step 2 :The integral of the function from 0 to 5 is \(20 - 7 \log(6)\).
Step 3 :\(\boxed{20 - 7 \log(6)}\) is the final answer.