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