1. The problem is to factorize the expression $$25x^2 - 36y^2$$. 2. This is a difference of squares, which follows the formula $$a^2 - b^2 = (a + b)(a - b)$$. 3. Identify $$a$$ and $$b$$: here, $$a = 5x$$ because $$(5x)^2 = 25x^2$$, and $$b = 6y$$ because $$(6y)^2 = 36y^2$$. 4. Apply the difference of squares formula: $$25x^2 - 36y^2 = (5x + 6y)(5x - 6y)$$. 5. Therefore, the correct factorization is option C: $$(5x + 6y)(5x - 6y)$$.