iPhone 5 dropped in water - shows this message when booted

Mitch, first things first. Shaking a phone and placing it in Rice is the absolute wrong thing to do. One might as well not do anything. So start by cleaning your board and your connectors asap. You will get corrosion damage if you do not fix that properly. The very first step I would take is to disassemble your phone. Use these guides to disassemble your phone. Take a careful and close look at all components and connectors. Truly assess the damage. Look for corrosion, evaluate the pins in the connectors etc,. Take a look at all connectors as well as cable ends. Remove all the EMI shields. Once you got the gross contamination cleaned, use 90%+ isopropyl alcohol and clean your parts some more. For a proper cleaning, use this guide. It was written for a Apple iPhone 3G but it is still pertinent to your phone as well. I can not stress the importance of a good cleaning enough, so do it over and over while replacing the alcohol after each cleaning. Do not use compressed air for the cleaning since that can drive liquid as well as corrosion particles into areas that will cause trouble later on. The importance here is the cleaning. You can also dry the board at ~220F in an oven for a couple of hours after the cleaning. If you can get it professionally cleaned in an ultrasonic cleaner, then that is of course the best way to go. Do not forget to replace the battery. This is a must and not an option. It will fail if you do not take care of it now.

As for your error screen, those are NAND errors. Anytime your phone restarts, it does something like a hardware check. So if any off your hardware does not respond your phone will display this message. It can be a benign as a broken flex to more sinister things like rear/front camera etc. You do want to start the phone with a minimum off peripherals, i.e. good dock connector, good battery, good display and see if it starts ok. Then add each peripheral and see which one gives you that error. Make sure that you turn your phone off each time you add some component. Keep in mind that water damage is the hardest to troubleshoot and to repair. Whatever you do stay away from RICE