I don't know what a counter is, so I'll just use object.

The question is the same as asking "Five objects are drawn. What is the probability that there is a win among the 2nd through 5th draws?" This is because a given draw is independent from any preceding draws.

So using my equivalent problem, it's the probability that a win is obtained on the 2nd draw, plus the probability of a win on the 3rd draw given that the 2nd draw was a loss, plus the probability of a win on the 4th draw given that the previous draws were losses, plus the probability that the 5th draw is a win given that the previous draws were losses.