I have a set of five equations which can be described as follows:

$m_{i}=\frac{k_{1}}{(x+a)^{i}} + \frac{k_{2}}{(b+d)^{i}}+ \frac{k_{3}}{c^{i}}$

for i=1 to 5 where $$\eqalign{ k_{1}&=\frac{a(x+a-b-c-d)+c(b+d)-xd}{(x+a-b-d)(x+a-c)} \\ }$$ $$\eqalign{ k_{2}&=\frac{x(d-c)}{(x+a-b-d)(b+d-c)} \\ }$$ $$\eqalign{ k_{3}&=\frac{xb}{(b+d-c)(x+a-c)} }$$

$m_{i}$, $i$=1 to 5 are constants and $x,a,b,c,d$ are variables.

I want to find $x,a,b,c,d$ satisfying these equations.