If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly two addresses is:

We need to find the probability that three letters posted to 5 addresses go to exactly two addresses.

We start by counting the total outcomes. Each letter can go to any of 5 addresses independently, so total ways = $$5^3 = 125$$.

Next, we count the favorable outcomes where exactly two addresses are used. We first choose which 2 addresses: $$\binom{5}{2} = 10$$ ways.

Then we count surjective maps from 3 letters to 2 addresses. Total ways to post 3 letters to 2 addresses = $$2^3 = 8$$. From these, we subtract the cases where all letters go to the same address, of which there are 2, giving $$8 - 2 = 6$$.

Therefore, the total favorable outcomes = $$10 \times 6 = 60$$.

Substituting these values into the probability formula gives $$P = \frac{60}{125} = \frac{12}{25}$$.

The correct answer is Option B: $$\frac{12}{25}$$.