Find the ordered quintuplet (a,b,c,d,e) that satisfies the system of equations
a + 2b + 3c + 4d + 5e = 41
2a + 3b + 4c + 5d + e = 57
3a + 4b + 5c + d + 2e = 34
4a + 5b + c + 2d + 3e = 63
5a + b + 2c + 3d + 4e = 15
