Go with the 5s. The only downside is that they start slowing down the older phones to encourage you to upgrade, so you might find yourself dissatisfied with the 5 (especially) pretty quickly if you don't get a new phone.
I personally have pretty small hands and I have the 5s. If I had to make the choice again there is no doubt in my mind that I would pick the 5s again. The 6 and especially the 6 plus are just too big for me. Also the extreme thinness of them sort of freaks me out. I think if you went with the 5s you would be happy with it.