The probability of hitting the target is given as 3/5. Let's assume that each attempt is independent of the others.

To find the probability that A hits the target exactly 2 times in 5 attempts, we need to consider the different ways in which this can happen.

Using Binomial Distribution:
We can use the binomial distribution to solve this problem. The binomial distribution is used to calculate the probability of a certain number of successes in a fixed number of independent Bernoulli trials, where each trial has the same probability of success.

The probability of getting exactly k successes in n trials can be calculated using the formula:

P(X=k) = C(n, k) * p^k * (1-p)^(n-k)

Where:
- P(X=k) is the probability of getting exactly k successes
- C(n, k) is the number of ways to choose k successes from n trials (combination)
- p is the probability of success in a single trial
- (1-p) is the probability of failure in a single trial
- n is the number of trials

Calculating the probability:
In this problem, we want to find the probability of hitting the target exactly 2 times in 5 attempts. So, we have:
- n = 5 (number of trials)
- k = 2 (number of successes)
- p = 3/5 (probability of success in a single trial)
- (1-p) = 2/5 (probability of failure in a single trial)

Using the binomial distribution formula, we can calculate the probability as:

P(X=2) = C(5, 2) * (3/5)^2 * (2/5)^3

Calculating the combination:
The combination C(n, k) can be calculated using the formula:

C(n, k) = n! / (k! * (n-k)!)

where "!" denotes factorial.

In this case, we have:
- n = 5 (number of trials)
- k = 2 (number of successes)

So, the combination can be calculated as:

C(5, 2) = 5! / (2! * (5-2)!)
= 5! / (2! * 3!)
= (5 * 4 * 3!) / (2! * 3!)
= (5 * 4) / 2
= 10

Substituting the values:
Now, we can substitute the values into the binomial distribution formula:

P(X=2) = 10 * (3/5)^2 * (2/5)^3

Simplifying the expression, we get:

P(X=2) = 10 * (9/25) * (8/125)
= (10 * 9 * 8) / (25 * 125)
= 720 / 3125

Therefore, the probability that A hits the target exactly 2 times in 5 attempts is 720/3125, which is equivalent to 144/625.

So, the correct answer is option D: 144/625.