Let u, v, and w denote the lengths of three separate line segments. In

For U,V,W to become the lengths of the sides of the triangle, they must satisfy the two conditions

1). The sum of any two sides of a triangle is always greater than the third side
2). The difference between any two sides of a triangle is less than the third side

statement 1:

u,v,w ==> u,u+5, v

5< v< 2u+5

So, V is always greater than an unique value (5). SUFFICIENT

Statement2:

7-2<v<7+2

5<v<9

So, V is always greater than an unique value (5). SUFFICIENT

Both are sufficient alone. Hence,D

The sum of two sides of a triangle must exceed the third side. So if one side is u, and the other is u+5, the third side will clearly need to be larger than 5, so that when we add u and the third side, we get something that exceeds u + 5. So I imagine the intended answer is D here.

But that value 5 is not at all unique. Certainly v must exceed 5, but it also must exceed 4, or √2, or 0.01. For information to be sufficient in a DS question asking for a value, you need to be able to find a unique numerical answer for that value, and you can't do that here. I see a lot of prep company DS questions that ask, in various ways, for minimum or maximum values, and that type of question logically doesn't make sense as a DS question. There's a reason no official DS questions are set up this way.