Step 1: Run Backuptrans iPhone SMS + MMS to Android Transfer and connect both your Nexus 5 and iPhone to computer with USB cable. Then the software will find devices connected and automatically show them in the Devices list.
Step 2: Click the iPhone in Devices list. Turn to top toolbar and press "Transfer iPhone SMS + MMS to Android" button.
Step 3: Select target Android (Nexus 5) to save messages. Click Confirm to continue.
Step 4: Go to your Nexus 5 screen and then click "YES" to set Backuptrans app as your Nexus default SMS app.
Note: It will resume your default Messaging app(Hangouts) settings after transferring messages to Android.
Step 5: Back to the Backuptrans iPhone SMS + MMS to Android Transfer software on computer, and click "OK" to start transferring messages to Nexus 5.
Step 6: Transferred successfully. Now please go to your Nexus 5 and then click "YES" to resume your default Messaging app(Hangouts) settings.
Watch Video:
Done! Free download Backuptrans iPhone SMS + MMS to Android Transfer on your computer to have a try.
Note: If you are using Mac, please download Backuptrans iPhone SMS + MMS to Android Transfer for Mac instead.
Best luck!