Given information:
- There are 4 balls of unknown colors in a bag.
- A ball is drawn at random from the bag and is found to be green.
- The probability that all the balls in the bag are green is p.

Approach:
To find the value of 5p, we need to determine the value of p first. We can use the concept of conditional probability to solve this problem.

Conditional Probability:
Conditional probability is the probability of an event occurring given that another event has already occurred. In this case, we want to find the probability that all the balls in the bag are green given that one ball has already been drawn and found to be green.

Solving the problem:
Let's consider the different cases for the colors of the remaining three balls in the bag.

Case 1: All three balls are green
If all three balls are green, the probability of drawing a green ball in the first draw is 1. Since there are no other colors in the bag, the probability that all balls in the bag are green is 1.

Case 2: Two balls are green, one ball is not green
If two balls are green and one ball is not green, there are three possible scenarios for the non-green ball. The probability of drawing a green ball in the first draw is 2/4 = 1/2. The probability of drawing a non-green ball in the second draw is 1/3. Therefore, the probability that two balls are green and one ball is not green is (1/2) * (1/3) = 1/6.

Case 3: One ball is green, two balls are not green
If one ball is green and two balls are not green, there are three possible scenarios for the green ball. The probability of drawing a green ball in the first draw is 1/4. The probability of drawing a non-green ball in the second draw is 3/3 = 1. Therefore, the probability that one ball is green and two balls are not green is (1/4) * 1 = 1/4.

Case 4: All three balls are not green
If all three balls are not green, there are three possible scenarios for the colors of the three balls. The probability of drawing a non-green ball in the first draw is 3/4. The probability of drawing a non-green ball in the second draw is 2/3. Therefore, the probability that all three balls are not green is (3/4) * (2/3) = 1/2.

Calculating p:
To find the value of p, we need to add up the probabilities of all the cases where all balls are green. From the above analysis, we have:
p = 1 + (1/6) + (1/4) + 0 = 1 + 1/6 + 1/4 = 31/12

Calculating 5p:
To calculate 5p, we multiply p by 5:
5p = 5 * (31/12) = 155/12 = 12 + (11/12) = 1 + 1 + 1 + 1 + 1