No, the national broadband network (NBN) and 5G are two separate technology types, though both allow you to connect to the internet. The NBN is government-owned infrastructure that has been rolled out across the country by NBN Co. It uses fibre, and existing copper wire, to connect homes to the NBN. For more rural and remote areas of Australia, NBN Fixed Wireless and Sky Muster satellite are used.
5G infrastructure is owned by the telcos, primarily Telstra and Optus. 5G home internet offers another way for Australians to connect to the internet, though its availability is far behind that of the NBN, with 5G coverage being best in the capital cities. Rather than using fibre or copper to connect you to the internet, 5G connects you over a wireless network.