To find the probability of getting a sum of 12 when tossing five coins marked as 2 and 3, we can use the concept of generating functions.

Step 1: Define the Generating Function
Let's define the generating function for the first coin, marked as 2, as:
f(x) = x^2 + 1

Similarly, for the second coin, marked as 3, the generating function is:
g(x) = x^3 + 1

Step 2: Find the Generating Function for the Sum of Five Coins
To find the generating function for the sum of the five coins, we need to multiply the generating functions of each individual coin.

h(x) = f(x) * f(x) * f(x) * g(x) * g(x)
= (x^2 + 1) * (x^2 + 1) * (x^2 + 1) * (x^3 + 1) * (x^3 + 1)
= (x^2 + 1)^3 * (x^3 + 1)^2

Step 3: Find the Coefficient of x^12
To find the probability of getting a sum of 12, we need to find the coefficient of x^12 in the generating function h(x).

Expanding the generating function, we get:
h(x) = (x^2 + 1)^3 * (x^3 + 1)^2
= (x^2 + 1)(x^2 + 1)(x^2 + 1)(x^3 + 1)(x^3 + 1)
= (x^2 + 1)(x^2 + 1)(x^2 + 1)(x^6 + 2x^3 + 1)

Now, we can find the coefficient of x^12 by multiplying the coefficients of x^2, x^2, x^2, x^6, 2x^3, and 1 in the expanded form of h(x).

The coefficient of x^2 is 1, and the coefficient of x^6 is 1. The other terms do not contribute to the coefficient of x^12.

Therefore, the coefficient of x^12 is 1 * 1 = 1.

Step 4: Find the Probability
The probability of getting a sum of 12 is equal to the coefficient of x^12 divided by the sum of the coefficients of all terms in the generating function.

In this case, the sum of the coefficients is (1 + 1) * (1 + 1) * (1 + 1) = 2^3 = 8.

Therefore, the probability of getting a sum of 12 is 1/8.

Step 5: Simplify the Probability
The probability can be simplified as follows:
1/8 = (1/2) * (1/2) * (1/2)
= (1/2)^3
= 1/8

Therefore, the probability of getting a sum of 12 when tossing five coins marked as 2 and 3 is 1/8, which is equivalent to option E) 5/16.