Solution for a system of PDEs

I recently came across a system of PDEs
$frac{partial S}{partial z}= f_1(x,y,z,w,t)$,
$frac{partial S}{partial w}= f_2(x,y,z,w,t)$,
$frac{partial S}{partial t}= f_3(x,y,z,w,t)$,
$S(x,y,1,1,1)=f_4(x,y)$,
where $S$ is an unknown function of five variables $x,y,z,w,t$ and $f_i$ are known.
The question is how to obtain a general solution for $S$?

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