Second Question about Reversing Equations

Here another similar question but more complicated than former:

$\displaystyle

\begin{cases}

& u=a^3+3b^2d+3bc^2+3ce^2+3d^2e+6abe+6acd \\

& v=b^3+3a^2d+3ae^2+3cd^2+3c^2e+6abc+6bde \\

& x=c^3+3a^2b+3ad^2+3b^2e+3de^2+6ace+6bcd \\

& y=d^3+3a^2e+3ac^2+3b^2c+3be^2+6abd+6cde \\

& z=e^3+3a^2c+3ab^2+3bd^2+3c^2d+6ade+6bce

\end{cases}$

I would interesting how many solutions when all variables are real numbers. And difference with when all variables are complex numbers.