Yes, Aranui 5 is fitted with internet access capability, allowing you to access Wi-Fi and connect your devices. Note that there is a cost to access the internet, depending on how much access you require. Prices start at approximately AUD $50. Please keep in mind that onboard Wi-Fi is generally slower than what you will be used to at home, and may not be available in all parts of the ship. It is generally available in communal areas however, including the bars and dining room.
While you are on the islands where there is a signal, you may also be able to use your mobile phone if you have international roaming engaged. This generally needs to be organised before you leave home with your telecommunications provider.