HMMT November 2010 U26

$w, x, y, z$ are real numbers such that

$$\begin{aligned} w+x+y+z & =5 \\ 2 w+4 x+8 y+16 z & =7 \\ 3 w+9 x+27 y+81 z & =11 \\ 4 w+16 x+64 y+256 z & =1 \end{aligned}$$

What is the value of $5 w+25 x+125 y+625 z ?$