1. Given $x=\frac{1}{2-\sqrt{5}}$. Then $x^{3}+3 x^{2}-5 x+1=$
From $x=\frac{1}{2-\sqrt{5}}=-2-\sqrt{5}$, we get $x+2=-\sqrt{5}$. Therefore, $(x+2)^{2}=5$, which means $x^{2}+4 x=1$.
Then $x^{3}+3 x^{2}-5 x+1=\left(x^{2}+4 x-1\right)(x-1)=0$.