**Problem:**
Given that for a binomial distribution b(n, p), np = 4 and variance = 4/3, we need to find the probability P(x > 5).

**Solution:**
To solve this problem, we will use the formula for the variance of a binomial distribution:

Variance = np(1-p)

Given that variance = 4/3, we can substitute the values into the equation:

4/3 = 4p(1-p)

Now, let's solve the equation for p:

4/3 = 4p - 4p^2

4p^2 - 4p + 4/3 = 0

Multiplying through by 3 to get rid of the fraction:

12p^2 - 12p + 4 = 0

Dividing through by 4 to simplify:

3p^2 - 3p + 1 = 0

Now, we can solve this quadratic equation for p using the quadratic formula:

p = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 3, b = -3, and c = 1:

p = (-(-3) ± √((-3)^2 - 4(3)(1))) / (2(3))

p = (3 ± √(9 - 12)) / 6

p = (3 ± √(-3)) / 6

Since the discriminant is negative, there are no real solutions for p. However, the equation does have complex solutions. We can approximate the solutions to be:

p ≈ 0.5 ± 0.2886751346i

Since p represents a probability, it must be a real number between 0 and 1. Therefore, the values of p are not valid in this case.

Since we cannot solve for the exact value of p, we cannot directly calculate the probability P(x > 5). However, we can use the fact that np = 4 to find an approximation for the probability.

Given that np = 4, we can solve for n:

n = 4/p

Substituting the approximated values of p, we get:

n ≈ 4 / (0.5 ± 0.2886751346i)

Simplifying the expression:

n ≈ 8 ± 4.618802153i

Since n must be a positive integer, the value of n is not a real number in this case.

Therefore, without the exact values of p and n, we cannot directly calculate the probability P(x > 5). Hence, the correct answer is that the probability cannot be determined with the given information.