LN = natural log (
http://en.wikipedia.org/wiki/Natural_logarithm)
In Excel, to get the natural log of 5,000 you would enter the formula =LN(5000)
If a trading system has a 60% win rate and you want to know what the expected maximum number of consecutive losses over 5,000 trades is you would enter the following in Excel:
=(LN(5000)/-(LN(1-0.6))
As for the question "How did I derive this formula?" I didn't. That was derived many years ago by someone in the field of probability theory.
Regarding the comment about having an edge, as was stated already, unless you have a 100% win rate you will have consecutive losses and the maximum number of expected consecutive losses is a function of the number of trades and the win rate.
You may want to watch this video of Nick Radge addressing a group of traders (
http://www.youtube.com/watch?v=ew1L6SLpHgM). Nick uses the above formula at the 23:00 minute mark but he has a mistake in it which he is aware of.