\[\left\{\begin{matrix} x-y+z=3 & & \\ x^2+y^2+z^2=5 & & \end{matrix}\right.\]
Let \(x,y\) and \(z\) be real numbers satisfying the system of equations above, find the product of minimum and maximum of the expression below:
\[P=\frac{x+y-2}{z+2}.\]

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