iphone 5 touch screen is not working properly.

To make sure that this is not software related, set it up as new device, without using the latest backup, explained in this article:

Use iTunes to restore your iOS device to factory settings - Apple Support

If this does not work, your phone has to be serviced by Apple or an Authorized Apple Service Provider:

iPhone - Contact Support - Apple Support

IInteresting phenomenia I ran into. 5s / iOS 8.3 I have a simple latex rubber case, which I cleaned with dish detergent recently and wiped down my phone cuz it was pretty messy. Put it back together and noticed I couldn't select, swipe nothing, couldn't turn it off, had to force it to shutdown with powe/home buttons. I restarted it, reset it, restored it, no effect. Just for fun I took the case off it and VIOLA! full function! Put th case on, nothing, took it off normal function. I remembered how the case had felt a little slippery, dusty when I bought it so I rubbed a tiny amount of talcum powder around the inside of the case and I'm typing on it now so I guess it worked. I'm thinking I could use graphite dry spray too I'm not that thrilled with the talcum that close to my phone. I think the case without the barrier has full contact with the case and develops a static charge, perhaps when I cleaned it the I removed the barrier, or it picked up a static charge, like that science experiment we all did in middle school when you polarize a acitate rod with a piece of wool, at least we used to when there was money and teachers to do science experiments in middle school . . . guess they just take tests and talk about taking tests these days :-)