(Answer: when $k=-1$, the three roots are $2,1 \pm 2 \mathrm{i} ;$ when $k=3$, the three roots are $-2,-1$ $\pm 2 \mathrm{i}$)
(5) For the real-coefficient equation $x^{3}+2(k-1) x^{2}+9 x+5(k-1)=0$, one of the roots has a modulus of $\sqrt{5}$. Find the value of $k$, and solve this equation.