AMC 10 2021b Problem 15

The real number $x$ satisfies the equation $x+\frac{1}{x} = \sqrt{5}$. What is the value of $x^{11}-7x^{7}+x^3?$ $\textbf{(A)} ~-1 \textbf{(B)} ~0 \textbf{(C)} ~1 \textbf{(D)} ~2 \textbf{(E)} ~\sqrt{5}$