Is this iPhone 5 still salvageable?

I dropped my iPhone 5 in a lake and it was under water for about 10 minutes. I didn't put it in a bag of rice, but I did let it sit for about 25 days. When I connect it to a charger, it charges itself and turns on after a few minutes. Then it shuts off a little bit later, while still on the charger.

Is it too late to try the rice bag trick?

You can still try it, and hopefully it will work, but it's not likely that it will.
Change the rice daily for the next 3-5 days. DO NOT TURN ON THE PHONE DURING THE PROCESS, IT WILL RUIN THE CIRCUIT.

Best of luck.