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In the diagram, each square is composed of smaller squares with a side length of 1.

(1) Observe the diagram and fill in the table with the following information: \frac{}\frac{}
(2) In a square with a side length of n (n≥1), let the number of red small squares be P_{1} and the number of white small squares be P_{2}. Is there an even number n such that P_{2}=5P_{1}? If it exists, please provide the value of n; if it does not exist, please explain why.