The augmented matrix of a linear system has been reduced by row operations to the form shown. Continue the appropriate row operations and describe the solution set of the original system.

$\left[\begin{array}{ccccc}1& -1& 0& 0& -5\\ 0& 1& -3& 0& -4\\ 0& 0& 1& -2& 2\\ 0& 0& 0& 1& 3\end{array}\right]$

Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

A$.$ The solution has infinitely many elements.

B$.$ The solution set is empty.

C$.$ The solution set contains one solution:

$($Type integers or simplified fractions.$)$