Find the ordered quintuplet (a,b,c,d,e) that satisfies the system of equations
\begin{array}{rcrcrcrcrcr}
a & + & 2b & + & 3c & + & 4d & + & 5e & = & 41, \\
2a & + & 3b & + & 4c & + & 5d & + & e & = & 15, \\
3a & + & 4b & + & 5c & + & d & + & 2e & = & 34, \\
4a & + & 5b & + & c & + & 2d & + & 3e & = & 68, \\
5a & + & b & + & 2c & + & 3d & + & 4e & = & 57.
\end{array}
