Hi,
As you know water and electronics and electricity are not a good mix.
The water causes corrosion and provides circuit paths for the electricity which were not in the phone's operating design and could damage the components.
Rice is good to eat but it does nothing to fix the problem of corrosion
First you need to remove the battery as soon as possible from the phone
Here is a link to the Ifixit guide on how to replace the battery and also the LCD screen which should give you reasonable access to the phone's components.
iPhone 5s
Then you need to dis-assemble the rest of the phone and clean all the affected parts using Isopropyl Alcohol 90%+ to remove all traces of corrosion and water.
Here is a link that in general, describes the process.
Electronics Water Damage
You will probably have to replace the battery as it is very hard to recover a battery from water damage.
As always with electronics, especially surface mounted PCBs be gentle when handling and especially when brushing away the corrosion. You do not want to remove any components from the board.
Hopefully after you have done all this the phone might possibly work correctly again.
If this process seems too daunting, take your phone to a reputable, professional phone repair service and ask for a quote for a repair. If you decide to do this, do it sooner than later.