Step 1 :The original function is \(f(x)=x^{5}\).
Step 2 :A shift to the left by 1 unit would result in the function \(f(x)=(x+1)^{5}\).
Step 3 :A vertical compression by \(\frac{1}{3}\) would result in the function \(f(x)=\frac{1}{3}(x+1)^{5}\).
Step 4 :A reflection over the y-axis would result in the function \(f(x)=\frac{1}{3}(-x+1)^{5}\).
Step 5 :\(\boxed{\text{The correct answer is D. } f(x)=\frac{1}{3}(-x+1)^{5}}\)