Hello tiredofnotunderstanding,
There are a couple of ways to get the photos off of your iPhone 5 en masse, depending on how those photos were added to your iPhone 4s.
If they were taken with the iPhone 4s, then you can import them to your computer, choosing to delete the images after they've been imported.
Windows 8: Learn how to import photos and videos from a camera, phone, or DVD (Windows Help)
Windows 7 and Windows Vista: Learn how to get pictures from your camera to your computer (Windows Help)
Import photos and videos from your iPhone, iPad, or iPod touch to your Mac or Windows PC - Apple Support
If they were synced from iTunes to your iPhone 5s, the next set of steps can help remove them from your iPhone 5.
- Create a folder on the computer that you now sync with, and add a single photo to that folder.
- In the Photos tab in iTunes, click the box next to "Sync Photos From."
- In the pop-up menu next to "Sync Photos From," choose the folder you created in step 1.
- Apply the change.
- Uncheck "Sync Photos From."
- Apply the change again.
- Your synced photos will now be removed from the device.
Delete photos and video synced from iTunes when you can’t access the originals - Apple Support
Cheers