Permutated Pooled Pascal (Power of 5)

Algebra Level 2

(1+2+3+4+5)1+5(1+2+3+4)2+10(1+2+3)3+10(1+2)4+5(1)5= ? \begin{aligned} && { (1+2+3+4+5) }^{ 1 } \\ & +& 5 { (1+2+3+4) }^{ 2 } \\ & +&10{ (1+2+3) }^{ 3 } \\ & +&10{ (1+2) }^{ 4 } \\ & +&5{ (1) }^{ 5 } \\& =& \ ? \end{aligned}

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