Which inequality has no real-number solution?

Correct answer: (x+2>x+5)

To determine whether an inequality has real solutions, simplify it and check whether the resulting statement can be true. If the variable cancels and a false numerical statement remains, no value of the variable can satisfy the inequality.

In option A, subtracting \(x\) from both sides gives \(2>5\), which is false. Therefore there is no real number satisfying it. For comparison, option B becomes \(2<5\), which is always true, and option C becomes \(2\le5\), also always true. Option D is \(x+2\ge x+2\), an identity true for every real number. Hence option A is the only no-solution inequality.