To solve this equation, we first need to expand the left side of the equation using the square of a binomial formula:

(2x + 5)^2 = (2x + 5)(2x + 5)
= 4x^2 + 10x + 10x + 25
= 4x^2 + 20x + 25

Now, we set the expanded equation equal to 0:

4x^2 + 20x + 25 = 0

Next, we will solve this quadratic equation by factoring or using the quadratic formula:

We can see that this quadratic equation can be factored as a perfect square trinomial:

(2x + 5)(2x + 5) = 0
(2x + 5)^2 = 0

Since a square cannot be negative, the only way for the left side to be equal to zero is if each term inside the parentheses is zero:

2x + 5 = 0
2x = -5
x = -5/2

Therefore, the solution to the equation (2x + 5)^2 = 0 is x = -5/2.