Tap Settings > General > About.
Wait for the following alert to appear:
Tap OK to install the update.
Hold the Sleep/Wake button down until you see "slide to power off".
Slide to power off.
After the device powers off, hold the Sleep/Wake button to turn your phone back on.
Note: To finish the installation of the update, your iPhone 5 must be turned off and then on again.
After your iPhone restarts, tap Settings > General > About, then scroll down to Carrier and verify that "Verizon 13.1" is displayed.