It'd be nice to draw it to full scale to demonstrate the effect of even small waves blocking the horizon, but I have no such skill at rendering.

It would be near impossible to get the picture to scale. The angles would be imperceptible.

I'm not sure how much small waves would effect the view on a flat earth. In order to block the road, the waves have to rise above the line which connects the telescope to the opposite shoreline. This line has a slope of 6/(5*5280)=1/4400. So I guess a modest wave of a half a foot or so could potentially block the road if it was located somewhere within 2200 feet from the shore. But, then again we don't know how high the road is above the water, or how high those trees are.

For the round earth prediction, I'll use an Earth radius of 3960 miles. 5 miles subtends 1/792 radians. To calculate angle between the observer and where a line of sight meets the water at a point of tangency, I'll take arcos((3960/(3960+6/5280)) = 1/1320 radians. I'll subtract this from the total angle subtended to obtain 1/792-1/1320 = 1/1980 radians. I'll now take the cosine of this, divide the Earth's radius by it, and subtract an Earth's radius to obtain the total height blocked by the curvature of the earth, 3980/cos(1/1980) - 3960 =.00050505 miles = 2.667 feet = 32 inches.

So according to RE, anything within 32 inches above water on the opposite shore will be blocked from view. That's not much at all. I don't think its enough to block the road by itself, let alone the trees too.

Clearly, there is something else at play here. It could be waves. It could be refraction. But honestly, as much as I hate to say it, I don't think this evidence supports either model. In addition, this shows the subtleties involved with such measurements of the Earth on these scales and perhaps how unreliable they can be.