After expanding you get x2+10x+25, what two binomials multiply to give you that trinomial?

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).