5. The system of equations
$$
\left\{\begin{array}{l}
\sqrt{x+\frac{1}{y}}-\sqrt{x+y-3}=\sqrt{3}, \\
2 x+y+\frac{1}{y}=6
\end{array}\right.
$$

has the solution set $\qquad$
The answer: $(x, y)=(2,1)$ or $(4,-1)$.