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Find the ordered quintuplet (a,b,c,d,e) that satisfies the system of equations a+2b+3c+4d+5e=177,
2a+3b+4c+5d+e=154,
3a+4b+5c+d+2e=146,
4a+5b+c+2d+3e=138,
5a+b+2c+3d+4e=165

This a really hard questioon but don't give up, please.

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