How do I get my pictures off my Iphone 5s

Several ways:

Move them to your computer

Use a cloud service such as OneDrive, Google Drive or Carbonite

Move them via a computer to an external hard drive

Import photos and videos from your iPhone, iPad, or iPod touch to your computer - Apple Support

sdmcgill1 wrote:

How do I get my pictures off my Iphone 5s

By far the easiest way is to enable iCloud Photos in Settings/iCloud. Then your pictures will automatically be uploaded to your iCloud account as soon as they are taken. You can view or download them by logging in to https://icloud.com, or, if you have a Mac, they will automatically be transferred to the Photos app. And they will stay in sync between your iOS device(s) and your iCloud account or Mac.

You can also subscribe to Google Photos, and install the Google Photos app. It will also upload your photos automatically to your Google Photos account.

There are other solutions, such as upthere.com, which will automatically sync your photos, music and documents to your upthere.com account. Plus the excellent suggestions made by ManSinha.