No, that number isn't right. I think the second exponent in your equation needs to be a multiplier. But it's not an easy problem. I would phrase it this way: the chances of not being hit 5 or more times in a row ( because it's not just 5 times) is equivalent to 1-(all chances of being hit four times) - (all chances of being hit 3 times) - (all chances being hit 2 times) - (all chances being hit one time) - (all chances being hit no times). And then figure out the individual chances for each of those.
Here's one explanation that makes some sense to me:
So for your case, let's assume 50% avoidance. The probability of (5) consecutive hits is .5^5, or .03125 - meaning that the chance of this not happening is .96875. The chance that you will get a run of 5 hits in 100 runs is .0417, or 4%. But I think that's not quite right.The probability of "n" consecutive heads is .5 ^ n. So for 10 consecutive flips, the probability is .5 ^ 10 or 0.0009765625. The probability of this not happening is 1 - (.5 ^ 10) or 0.999023438.
The probability of not seeing 10 heads in a row can be expressed as (0.999023438) ^ #attempts. Thus at toss 710, it becomes more likely than not that you will have seen at least one run of 10 heads -- (0.999023438 ^ 710 = 0.499724591). If you toss the coin 5,000 times you will see at least one run of ten heads 99.3% of the time. If you toss the coin 10,000 times you will see at least one run of ten heads 99.9942882% of the time.
There's more details and a spreadsheet here: