To simplify the expression (25a^2 - 4c^2) / (5a + 2c), we need to factor the numerator and denominator first.

Numerator: 25a^2 - 4c^2
This is a difference of squares, which can be factored into (5a + 2c)(5a - 2c).

Denominator: 5a + 2c
This is already in factored form.

Now we can rewrite the expression with the factored numerator and denominator:

(5a + 2c)(5a - 2c) / (5a + 2c)

Now, we can cancel out the common factor of (5a + 2c) in the numerator and denominator:

= 5a - 2c

Therefore, the simplified expression is 5a - 2c.