Here another similar question but more complicated than former:
I would interesting how many solutions when all variables are real numbers. And difference with when all variables are complex numbers.
The solution in the complex case will be similar to the previous problem. Let , and for k=0,1,2,3,4 let
Then , and it follows that
Each has three complex cube roots, and there are five of them, giving a total of complex solutions. The number of real solutions is much more problematic. It's not clear to me whether there will be any at all.