My iPhone 5 says this cable may not support this device

Water damage can cause failure in a ton of different ways, but I'll try to point out a few.

1) Putting your phone in rice does little to nothing. It's possible you've gotten a bit of rice or some of its dust into the charge port, interrupting it's connection. Clean with a toothbrush and isopropyl as thoroughly as possible, allow to dry (10 minutes) and try again.

2) If this doesn't help, the port itself may have been damaged. This is any easy repair, do a quick search for the part and guide on this site.

3) If none of these work, then I'd move to board level damage. Feel for hot spots on the phone, and check for burned or missing components on the board. Replace or clean if possible.

Good luck!