AMC 10B Spring 2021 (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}

\text{(A)}\;-1

\text{(B)}\;0

\text{(C)}\;1

\text{(D)}\;2

\text{(E)}\;\sqrt{5}