As you now know, water and electronics and electricity are not a good mix.
The minerals in the water cause corrosion and the water also provides circuit paths for the electricity which were not in the phone's operating design and could damage the components. The corrosion process starts immediately and will not stop until it has been thoroughly cleaned away
Rice is good to eat but does nothing to fix the problems caused by corrosion.
Don't Put Your Device in Rice. Here's Why
First do not turn on your phone and then you need to with the phone turned off, remove the battery as soon as possible from the phone to minimize further damage.''
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. Do not use "rubbing alcohol" as in some cases this is only 70% or less and is not as effective. If you do check the label to verify the amount
Here is a link that describes the process.
Electronics Water Damage
There is also this link that in general describes how to hopefully repair liquid damage to an iPhone.
Repairing iPhone Liquid 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.
Here is a link to the Ifixit repair guide(s) for an iPhone 5s that may help you
iPhone 5s Repair
If this process seems too daunting, take your phone to a reputable, professional mobile phone repair service experienced in water damage repair and ask for a quote for a repair. If you decide to do this, do it sooner than later.