+218 Find the ordered quintuplet $(a,b,c,d,e)$ that satisfies the system of equations
\( \begin{array}{rcrcrcrcrcr} a & + & 2b & + & 3c & + & 4d & + & 5e & = & 47, \\ 2a & + & 3b & + & 4c & + & 5d & + & e & = & 15, \\ 3a & + & 4b & + & 5c & + & d & + & 2e & = & 3, \\ 4a & + & 5b & + & c & + & 2d & + & 3e & = & 26, \\ 5a & + & b & + & 2c & + & 3d & + & 4e & = & 29. \end{array}\)
