Solve the radical equation. Check all proposed solutions. \[ x-\sqrt{4 x-15}=5 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Use a comma to separate answers as needed. Simplify your answer.) B. The solution set is $\varnothing$.

Step 1 ：Isolate the radical on one side of the equation: \(x = 5 + \sqrt{4x - 15}\)

Step 2 ：Square both sides of the equation to eliminate the radical: \((x - 5)^2 = 4x - 15\)

Step 3 ：Solve the resulting quadratic equation to get the proposed solutions: \(x = 4, 10\)

Step 4 ：Check the proposed solutions in the original equation: \(4 - \sqrt{4*4 - 15} = 5\) and \(10 - \sqrt{4*10 - 15} = 5\)

Step 5 ：Both proposed solutions are valid.

Step 6 ：Final Answer: The solution set is \(\boxed{4, 10}\)