Given that \(x,y,\) and \(z\) are real numbers that satisfy the following system of equations

\[x+y+z=5\] \[x^2+y^2+z^2=15\] \[xy=z^2\]

find the value of

\[\frac{1}{x}+\frac{1}{y}+\frac{1}{z}.\]

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