I think 5 generations is right. The thing is, every yeast washing session you can easily harvest enough for 2 batches so ...
You are completely right on that point. I took the yeast from my Bourbon County Stout clone. It was a half of a vial, pitched with a starter. I know that ideally you shouldn't harvest from super high gravity beers, but the yeast performed so well, and was done so quickly (within about 15 days), that I decided that I wanted to give it another opportunity.
I wound up with a full 1.75L of washed yeast slurry from that batch. And that's after pouring off the water and debris!!! Since I was brewing that night, I warmed up the yeast, put it into a 2L flask, added .3L of 1.010 wort (just enough to get them going again). By the time my AG batch was done 6 hours later, I had half an inch of krausen in the flask. I pitched half of that yeast and stuck the rest back in the fridge. I didn't even really aerate my wort because I was already pitching so much yeast, I figured the aerobic respiration phase probably wasn't all that critical. And, well... when I walked into my apartment 18 hours later after work, I freaked out. I smelled beer. My apartment reeked of beer. I was sure a corny blew, a blow off hit the ceiling, something... but no. All I found was my 1.081 IPA pounding the airlock like a beast. WHUMP-WHUMP-WHUMP-WHUMP!!!
My 2L flask has a solid 1.5 inches of yeast in it right now. And if you know how big a 2L flask is, you know that's a LOT of yeast. I'm tempted to split it into two or 3 batches because I think I'm getting close to over-pitching.
Man... paying $7 for a yeast you use one time is crazy when it's so easy to grow your own! In fact, you already do it every time you make beer!!! And given that you should be making starters anyway with liquid yeast, you should already have the equipment you need for culturing. And if you don't, a 2qt glass milk (or wine) jug, a drilled stopper, and some tin foil (or airlock, or foam stopper) is all you need... we're talking under five bucks! Although I do think it's easier to rinse yeast and repitch than it is to make a full starter. So actually, it's a time-saver to do that. And given that my average brew probably costs me twenty bucks, the yeast may be between a third and a seventh of the cost of a batch, and that cost is basically reduced to nothing. I hate to say that I'm cheap, but I'm not made of money. If I can cut out a third of my cost for a batch, I'll do it. Especially knowing that it actually makes the yeast more active and results in better fermentations.