$\sum_{x=0}^{5} b(x ; 12,8)$

Step 1 ：The problem is asking for the sum of binomial probabilities for x ranging from 0 to 5, given 12 trials and a probability of success of 8/12. The binomial probability formula is \(b(x ; n, p) = C(n, x) * p^x * (1-p)^(n-x)\), where C(n, x) is the combination of n items taken x at a time, p is the probability of success, and n is the number of trials.

Step 2 ：Let's substitute the given values into the formula: n = 12, p = 0.6666666666666666.

Step 3 ：By calculating, we get the total probability as 0.066447639531011.

Step 4 ：So, the sum of the binomial probabilities for x ranging from 0 to 5, given 12 trials and a probability of success of 8/12, is \(\boxed{0.066447639531011}\).