Probability of a certain sequence when rolling dices

I roll a dice 50 times. What is the probability that there is a(t least one) sequence of (at least) 5 consecutive sixes in the result?

For example, suppose somewhere in my sequence of 50 dice results, there is:

...46166666332...

Then it's a "hit" cause it contains 5 consecutive sixes.

I can't decide how to approach this: as a counting / combination problem, or as a probability problem. In either case I can't figure out how to avoid counting combinations or possibilities twice... :confused: