I've never seen a mower go to 5 inches. 4 should be fine. 5 would be nice as would 6 up to 9 inches.

If you want to talk about tall St Augustine, I'm the guy to talk to. I have a lawn in George West, TX which has not been mowed since October of 2011. In most shady parts it is 32 inches high. Most of the rest is about 12 inches (full sun) but some is not up to 8 inches in all this time. Water conservation is the issue I was addressing by stopping mowing. The parts of the lawn that are up to 32 inches have not been watered in months except for our sparse rainfall. One part has not been watered once since Oct 2011.

There is no thatch build up in any St Augustine no matter how high it gets UNLESS you water it every day and fertilize frequently with liquid fertilizers like Medina Hasta-Gro. That combination allows the entire grass plant to develop and survive on top of the soil - roots and all. If you follow our normal mantra of watering deeply once per (week or month) then you won't ever have thatch. Oh also feeding with dry fertilizer goes along with that.

Yellow at the tip? When you mow it should not have a tip left? You should have an end that looks like someone sliced it very cleanly with scissors. If it looks raggedy at all, then you need to sharpen the mower.

Here's a picture of my tall grass lawn. My dog is about 30 inches high at the tips of her ears. The grass had flopped over from being dry but it never showed any of the other signs of heat or drought stress.

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That picture was taken in April 2012. Note there is no sign of dormancy. I'm not sure why that was. Parts of the lawn did go dormant last winter but not the really tall grass.

I used to mow mine at 3 inches minimum usually in the spring then in the fall when we get cold weather rolling in.

It sounds like your lawn guy is looking for excuse not to change cutting height. Not sure which lawnmower he uses but the big ones depending on the brand/model, it can be a pain having to change the cutting height if pressed for time.