Evaluate the integral \(\int \frac{5}{t^6} \sin\left(\frac{1}{t^5} - 5\right) dt\)

Which of the following options correctly evaluates the integral?

A) \(\frac{-\cos\left(\frac{1}{t^5} - 5\right)}{t^5} + C\)
B) \(\frac{\cos\left(\frac{1}{t^5} - 5\right)}{t^5} + C\)
C) \(\frac{\sin\left(\frac{1}{t^5} - 5\right)}{t^5} + C\)
D) \(\frac{-\sin\left(\frac{1}{t^5} - 5\right)}{t^5} + C\)