Preflop: Call is good.
Flop: Check on the flop is fine. Villian has all combos of KKs,JJs,44s,KJs,AAs, we have none of those so check/calling is the only play.
Turn: I think we can bet this one. We can get calls from all Jx which checks/back, QQs, and some weak Qx. Doubt villain has many Ax in his range besides A,J.
River: I think we check this one. Possibly to check/call or even Check/raise probably just check/call though. Blockers to the straight with our Qx, top pair top kicker, Kx, and villian is very capped when he checks back flop so we should be able to get his weak Ax to fold to a big raise.

River I often just check and try to go to showdown. If we face a bet it never feels great but we should call as 2 pairs and AAA don't make that much sense and some obvious draws missed.

The worse your opponent is the more I like betting over check/calling the river in this spot and since this is NL5 anonymous table I think going for thin value is slightly better plan by default. That being said I can totally see check/calling in this spot.