System of equations

Consider the system of equations $$\begin{cases} x^3 - x^2 y = x^2 - x + y + 1, \\ 5\sqrt{x+2} + \sqrt{y+3} = 3x^2 - y + 1. \end{cases}$$ Find the sum of $x^2 + y^2$ over all real solutions $(x, y)$ of the system.