Q: how do you transfer pictures and videos from iphone 5s to computer?

One method is via USB cable: Import photos and videos from your iPhone, iPad, or iPod touch to your Mac or Windows PC - Apple Support

There are also 3rd party apps such as http://www.photosync-app.com

Or you can use Photo Stream (but only for new photos taken after you turn on Photo Stream) My Photo Stream FAQ - Apple Support

or via cloud services.

The cable and Windows worked fine for me until iOS 9. Since then I am unable to get Windows to recognize the iPhone 6 not does the import dialog window open like it used to do. The iPhone is seen in iTunes but not anywhere in Windows Explorer. I've tried quite a few times and different ways but cannot get Windows 7 to do the photo import anymore. The one app that used to work for this, Simple Transfer, now does not transfer all my pictures to the computer. A number of pictures are always missing using Simple Transfer since iOS 9. Also, videos used to be copied using either of these and now I have no way to copy videos to the computer. Any suggestions to get this done?

I am having this trouble as well.  The dialogue box is not coming up when I plug in my iphone 5S into the Windows 7 desktop. Itunes comes up but it is of no help in viewing photos on my phone.  And when my phone is plugged into the computer, it does not come up in the list of devices and/or drives attached to the computer.  Before the icon of my phone would show up in the list of attached devices and I could click on that to view the photos on my phone and download photos into whatever websites I wanted to download them on.