Evaluate $\int_{-1}^{1} 5 x^{4} \sqrt{x^{5}+1} d x$.
- A$\frac{4\sqrt{2}}{3}$
- B$\frac{2\sqrt{2}}{3}$
- C$\frac{8\sqrt{2}}{3}$
- D$\frac{\sqrt{2}}{3}$
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