A rectangular block has a square base of side \((\sqrt{10}+\sqrt2)\) cm and a height of \(h\) cm. The volume of the rectangular block is \((52+28\sqrt5)\text{ cm}^3\).
Without using a calculator, find the height of the rectangular block, in cm. Give your answer in the form \((a+b\sqrt5)\) cm where \(a\) and \(b\) are integers.[5]
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