MathNet 2014 Question 39

Do there exist real numbers $x,y,z$ such that $$\frac{x}{y}+\frac{y}{z}+\frac{z}{x}=-5\quad\text{and}\quad\frac{y^2}{x^2}+\frac{z^2}{y^2}+\frac{x^2}{z^2}=8?$$ (Ilko Brnetić)