You're aware that
... (x +a)(x +b) = x² +(a+b)x + ab
so
... (x +a)² = x² +2ax + a²
With this in mind, you notice that 25 is the square of a prime, so that is your first clue that the trinomial is a square. The last bit of information you need for that conclusion is that the coefficient of x satisfies
... 10 = 2√25 = 2·5
Now, you know ...
... x² + 10x + 25 = (x +5)² = (x +5)(x +5)
The two binomials are both (x+5).
