If the line y = mx + c is a tangent to  both the circle $x^2+y^2=5r^2$ and the parabola $y^2-4x-2y+4\lambda +1=0$ and the point of contact of the tangent with the parabola is (8, 5)
then the value of $25r^2+\lambda +2m-c$ is ______________ 

(8, 5) lies on parabola  $\Rightarrow \lambda =4$
Now the parabola equation is  ${(y-1)}^2=4(x-4)$
Equation of tangent is $y-1=m(x-4)+\frac{1}{m}$ 
(8, 5) lies on tangent  $\Rightarrow m=\frac{1}{2}$
Equation of tangent to parabola is $y=\frac{x}{2}+1 \Rightarrow c=1$  
Now  $y=\frac{x}{2}+1$ is a tangent to circle $\Rightarrow r=\frac{2}{5}$
$\therefore 25r^2+\lambda +2m-c=4+4+1-1=8$