I'm not sure how often we'll see a set here given Villain's flat on the turn to Hero's small bet – I'd expect to see a raise more often than not.

I think we need to bet bigger on the turn to get value from Villain's Ax.  In a $5r most Villain's will have a hard time folding top pair.  11111 feels good to me on the turn, and then we can bet the river on the smaller side if needs be to get an obligatory type call.

I'm not a good maths guy but I suspect his range is more weighted towards Ax combos when he calls the Cbet than 9x or 7x etc.  Discounting random floats for the time being, therefore, whilst our small turn bet may get more calls from the weaker part of his range, I think we'll make more overall going after the extra chips when he has Ax than betting smaller and targetting his whole range (he may fold turn anyway with 7x).  I'm not sure I've managed to get across what I'm trying to say here very well but hopefully this makes sense!  Of course you may not agree anyway since this is only my gut instinct.

I tend to think that small stakes Villains play too honest on Ace high flops and I'm not really giving them too much credit for random floats in a $5r, so thanks for posting as my thinking may be too simplistic.  Honestly, on the river I'm thinking wtf got there because I just don't see this line as a bluff ever (as I said it may be a hole in my thinking that I'm not giving enough credit to enough Villains!).  I guess I'm hoping he has AK!