STRATEGY: Upon reading any GRE Multiple Choice question, we should always ask, Can I use the answer choices to my advantage?
In this case, we can easily test the answer choices for equivalency.
Now let's give ourselves up to 20 seconds to identify a faster approach.
In this case, we can also try to simplify the expression so that it matches one of the answer choices.
I think testing for equivalency will be faster, so I'll go with that...

Key concept: If two expressions are equivalent, they must evaluate to the same value for every possible value of x.
For example, since the expression 2x + 3x is equivalent to the expression 5x, the two expressions will evaluate to the same number for every value of x.
So, if x = 7, the expression 2x + 3x = 2(7) + 3(7) = 14 + 21 = 35, and the expression 5x = 5(7) = 35

Let's test an easy value like \(x = 0\).
Plug \(x = 0\) into the given expression to get: \(0^2-7(0)+10 \times \frac{0+5}{0-2} = 10 \times \frac{5}{-2} = \frac{50}{-2} = -25\)

Now we'll plug \(x = 0\) into the five answer choices see which one(s) evaluate(s) to \(-25\)

(A) \(0^2 − 25 = -25\). GREAT! Keep.

(B) \(0^2 + 10(0)x + 25 = 25\). ELIMINATE

(C) \(0 + 5 = 5\). ELIMINATE

(D) \(0^2 +25 = 25\). ELIMINATE

(E) \(0^2+5 = 5\). ELIMINATE

Answer: A