Five Equations, Five Variables!

\[\large{\begin{cases} {a(b+c+d+e)=128} \\ {b(a+c+d+e)=155} \\ {c(a+b+d+e)=203} \\ {d(a+b+c+e)=243} \\ {e(a+b+c+d)=275} \end{cases}}\]

Five positive integers \(a,b,c,d,e > 1\) satisfy the above five equations. Find the value of \(\large{a^b + cd + e}\).

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