To solve this equation, we need to expand both sides and simplify.

Expanding the right side:
(2x + 1)^2 = (2x + 1)(2x + 1) = 4x^2 + 2x + 2x + 1 = 4x^2 + 4x + 1

Therefore, the right side can be written as:
(2x + 1)^2 = 4x^2 + 4x + 1

Now, substituting into the original equation:
7x^2 = 4x^2 + 4x + 1 + 3x^2 - 5

Combine like terms:
7x^2 = 4x^2 + 3x^2 + 4x - 5 + 1

Simplify:
7x^2 = 7x^2 + 4x - 4

Subtract 7x^2 from both sides:
0 = 4x - 4

Add 4 to both sides:
4 = 4x

Divide by 4:
x = 1

Therefore, the solution to the equation 7x^2 = (2x + 1)^2 + 3x^2 - 5 is x = 1.