Solve the system by elimination. \[ \begin{array}{r} 5 x+7 y=18 \\ 10 x-3 y=53 \end{array} \] The solution set is (Simplify your answer. Type an ordered pair.)

Step 1 ：Given the system of equations: \[\begin{array}{r} 5x+7y=18 \\ 10x-3y=53 \end{array}\]

Step 2 ：First, we multiply the first equation by 2 to get \(10x + 14y = 36\).

Step 3 ：Then, we subtract the second equation from the result to eliminate x, which gives us \(17y = -17\).

Step 4 ：Solving for y, we get \(y = -1\).

Step 5 ：Substituting \(y = -1\) into the first original equation, we get \(5x + 7(-1) = 18\), which simplifies to \(5x = 25\).

Step 6 ：Solving for x, we get \(x = 5\).

Step 7 ：Final Answer: The solution to the system of equations is \(\boxed{(5, -1)}\).