Circle

Consider a circle \(C_{1}: x^{2}+y^{2}-4 x-2 y=\alpha-5\). Let its mirror image in the line \(y=2 x+1\) be another circle \(C_{2}: 5 x^{2}+5 y^{2}-10 f x-10 g y+36=0\). Let \(r\) be the radius of \(C_{2}\). Then \(\alpha+r\) is equal to _________.