iPhone 5s: benefits of 64 bit processors if no more than 4 GB of RAM? My understanding is that the (main) reason of having a 64 bit processor, is to be able to use more than 4 GB of RAM.

In PCs, it is now very common to have more than 4GB of ram, and to really be able to use such ram, you NEED a 64 bit processor.

But for a smartphone, which (afaik) doesn't have more than 4GB of ram, what's the point? what is the benefit? 

What kind of apps benefit from it that will really make a difference ?

Specific examples of apps taking advantage would be nice.

Do final users will even notice a difference? Or is it just a marketing strategy?

Note, i know a similar question has been answered here: https://superuser.com/q/56540/152803
but in this one i ask specifically for smartphones, that one is focused on Intel/AMD architecture. Besides, that answer is now more than 4 years old...
My understanding is that the (main) reason of having a 64 bit processor, is to be able to use more than 4 GB of RAM.


Well, everything is 64 bits wide in a 64 bit CPU.  For one, computation involving large numbers is more efficient.

ARM introduced a few changes and improvements in the move to 64-bit.  


All 64-bit ARM CPUs have built in floating point.
Quite a few things were simplified, making it easier for compliers to create more optimized code.
The SIMD/floating point unit has more registers.  This means more data can be processed in operations that use SIMD (like media decoding) or floating point (anything with 3d graphics).
It also has a few built-in instructions for cryptography.  


Reference.


  But for a smartphone, which (afaik) doesn't have more than 4GB of ram, what's the point? what is the benefit? 


This is true now.  I'd bet in 3-5 years it won't.