+556 Find the ordered quintuplet (a,b,c,d,e) that satisfies the system of equations
\begin{array}{rcrcrcrcrcr}
a & + & 2b & + & 3c & + & 4d & + & 5e & = & 47, \\
2a & + & 3b & + & 4c & + & 5d & + & e & = & -15, \\
3a & + & 4b & + & 5c & + & d & + & 2e & = & -18, \\
4a & + & 5b & + & c & + & 2d & + & 3e & = & 3, \\
5a & + & b & + & 2c & + & 3d & + & 4e & = & 14.
\end{array}
\(\begin{array}{rcrcrcrcrcr} a & + & 2b & + & 3c & + & 4d & + & 5e & = & 47, \\ 2a & + & 3b & + & 4c & + & 5d & + & e & = & -15, \\ 3a & + & 4b & + & 5c & + & d & + & 2e & = & -18, \\ 4a & + & 5b & + & c & + & 2d & + & 3e & = & 3, \\ 5a & + & b & + & 2c & + & 3d & + & 4e & = & 14. \end{array}\)
