Solve the given system of equations. \[ \begin{array}{l} 5 x+4 y-5 z=-35 \\ 3 x-5 y+3 z=10 \\ 6 x-3 y+6 z=-15 \end{array} \] Select the correct choice below and fill in any answer boxes within your choice. A. There is one solution. The solution set is $\{(\square, \square, \square)\}$. (Simplify your answers.) B. There are infinitely many solutions. C. There is no solution.

Step 1 ：First, we represent the system of equations in matrix form. The matrix A is \[\begin{bmatrix} 5 & 4 & -5 \\ 3 & -5 & 3 \\ 6 & -3 & 6 \end{bmatrix}\] and the matrix B is \[\begin{bmatrix} -35 \\ 10 \\ -15 \end{bmatrix}\].

Step 2 ：We then solve the system of equations using the matrix method. The solution is \[\begin{bmatrix} -4 \\ -5 \\ -1 \end{bmatrix}\].

Step 3 ：Finally, we can conclude that the solution to the system of equations is \((-4, -5, -1)\). Therefore, the correct choice is A. The solution set is \(\boxed{\{(-4, -5, -1)\}}\).