when my choices if I call are split or lose, I'd have to have a VERY strong feel of a split. Something like 90% or more (and I don't see that here). It's pure risk vs. reward and the reward sucks.
I'm definitely betting that flop as it seems fairly ragged for someone who raised preflop. If I'm called then I'm slowing way down and letting go.
By betting the pot, you risk $5 and perhaps either win it there or find information on your opponent and hopefully check down to river. As you played it you've called 7.50 of bets and still don't really know where you are in the hand.
Out of position, I make my stand on the flop, not the river.
TR