Mash pH typically rises throughout the mash. I did a careful and frequent analysis of pH variation in my last brew session mash. I found an increase of about 0.1 units over the course of about 30 minutes. Since most enzymatic reactions occur in about the first 15 min of the mash, I’m most concerned with the pH then. That is one reason why Bru’n Water would predict a little low when compared with a late pH measurement.
The overall pre-boil wort pH into the kettle is a pretty important factor for good results. If your sparging water has excessive alkalinity and pH, that could pull up the kettle pH and create the opportunity to cause harshness in the perception and flavor. On the other hand, a brewer needs to avoid too low a pre-boil kettle pH. Colin Kaminski pointed out that low kettle pH tends to reduce hop expression and bittering. I agree with that finding.
My recommendation is that pre-boil kettle pH should fall in the 5.2 to 5.4 range. You can bump that up a tenth for dark beers to smooth them and down a tenth in light beers that you want crisper or tarter.