Found myself in a peculiar spot on the River and I was hoping to get some feedback:

Here's the hand:

Hero $200 (BB) dealt Td 5c

BTN min opens to $4

Hero calls

Flop ($8): Kd Jd 5h

Hero checks
BTN bets $4

Hero decides to check/raise with backdoor flush/straight (intending to barrel any diamond/broadway Turn). Also, it's a pseudo protection bet for my 5 since I'm OOP and I'd be happy to take down the pot and deny equity to high cards. It's a board I expect him to cbet near 100% so I feel like his range is very wide with plenty of high cards that leave me guessing on the Turn/River if I simply check-call.

Hero raises to $15
BTN calls.

At this point, I think he still calls a handful of 66-TT, Jacks which are the primary hands I'm trying to fold with barreling later on favorable Turns.

Turn ($38): Qd

Hero continues his plan and barrels. At this stage I don't think my 5 has much showdown equity but I've picked up good equity with both a diamond and card higher than the J. I expect to be able to fold out a lot of the 77-pair of Jacks range with a 2/3 pot-sized bet.

Hero bets $30
Villain calls $30

River ($98) 5s

We have a pot-sized bet left and now I've back-doored into a very disguised trips.

What is our preferred line in this spot and why? I'll include the result of the hand below.

I'd also like some thoughts on my general play with the hand. I tried to outline my logic and line of thinking above to try and get the best feedback. On one hand including Td5x (backdoor straight/flush draw) in my Flop check-raise range seems nice because I block a few additional hand combos that can continue (K5s, J5s, 55) but I wonder if using something like bottom-pair BDFD/BDSD makes my Flop check-raise frequencies far too high?

Spoilers

Hero opts to check and BTN jams. Hero calls.

BTN shows KK for Kings full of Fives.