There's a 1/3 chance that a single die will produce a 5 or 6. That means that there's a 2/3 chance that some other number will be the result. The chance is the same for each individual die.
For all 8 dice the chance of no 5 or 6 is (2/3)^8=3.9% approx. Therefore, there is a 100-3.9% chance that at least one 5 or 6 will be thrown: 96.1%.