What's the clear benefit of 64 Bit in iPhone 5s?

You can go and be technical with your terms.

It can process more bits and handle a bigger load. I'd much rather have a dual core processor that has a 64 bit than a quad core that has only 32 bit. 64 bits means more area to process information at one single time solely double the amount of a 32 bit processor. In all quad core or higher core devices including computers, phones, tablets a lot of the time the cores aren't being used. It evens out to be about 85% of the time only the first 2 cores are being used solely because processing of info must be in order, So if the first core processes one thing and the second core another then you need part 1 and 2 to process the third thing it will end up just going back to the first or second cores again.

The 64-bit refers to how many registers that the CPU can allocate for it's instruction set (more instructions) and memory addresses. If you would like to have a system that has over 4GB of memory then you will need a 64-bit system. As far as performance benefits now though you won't really see any except maybe in applications where encryption and decryption are performed. Actually, items in memory take up slightly more space in a 64-bit environment versus a 32-bit one which would be one disadvantage; the difference though is pretty minor. Don't worry about the bits as it is not important or going to affect you until we see more than 4GB or RAM used. Most ARM CPU's, especially those manufactured by Qualcomm for a couple years now, have been assigning 128-bit addresses for their NEON and other instruction sets that truly benefit or need them.

Apple has most likely done a great job balancing power and efficiency. This new chip is without a doubt much faster than it's predecessor but the end user will not be seeing the benefits of 64-bit CPU's likely for another year or two and you can be pretty sure that the Android platform will be the first to need it as that system is much more demanding on memory and has traditionally implemented more into their CPU's.