Mordan; I tried the same thing, but then went and killed Jake a couple times before and after maxing Axe Expertise. In both cases the character stats pane displayed the damage as 87-137 (the axe was 78-128).

Axe Expertise 0 = 85 to 130 range, 108 +/- 15 average and standard deviation
Axe Expertise 5 = 139 to 195 range, 162 +/- 16 average and standard deviation

I assume I got more that the expected extra average +36 damage since I was at a much higher level than Jake.