To solve this equation, we can expand both squared terms and simplify the equation:

(2a - 5)^2 - (2a + 3)^2 = -80

Expanding the squared terms:

(2a - 5)(2a - 5) - (2a + 3)(2a + 3) = -80

Simplifying further:

4a^2 - 20a - 20a + 25 - (4a^2 + 6a + 6a + 9) = -80

Combining like terms:

4a^2 - 40a + 25 - 4a^2 - 12a - 9 = -80

Simplifying:

-52a + 16 = -80

-52a = -96

a = 96/52

a = 24/13

Therefore, the solution to the equation is a = 24/13.